ANÁLISE CONJUNTA DE REGRESSÕES E PLANOS DE MELHORAMENTO

■❖▲❆ ▼❆❘■❆ ❙■▲❱➱❘■❖ P■◆❚❖

❆◆➪▲■❙❊ ❈❖◆❏❯◆❚❆ ❉❊ ❘❊●❘❊❙❙Õ❊❙

❊ P▲❆◆❖❙ ❉❊ ▼❊▲❍❖❘❆▼❊◆❚❖

❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ ●r❛✉ ❞❡ ❉♦✉t♦r ❡♠ ▼❛t❡♠át✐❝❛✲❊st❛tíst✐❝❛ ♣❡❧❛ ❯♥✐✈❡rs✐❞❛❞❡ ◆♦✈❛ ❞❡ ▲✐s❜♦❛✱ ❋❛❝✉❧✲ ❞❛❞❡ ❞❡ ❈✐ê♥❝✐❛s ❡ ❚❡❝♥♦❧♦❣✐❛✳

▲✐s❜♦❛

❆❣r❛❞❡❝✐♠❡♥t♦s

❆♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦ ❞❡ r❡❛❧✐③❛çã♦ ❞❡st❡ tr❛❜❛❧❤♦✱ ❛♣r♦❢✉♥❞❡✐ ❡ ❝♦♥s♦❧✐❞❡✐ ❝♦♥❤❡❝✐♠❡♥t♦s ❛❞q✉✐r✐❞♦s✱ r❡❛❧✐③❡✐ ♣❡sq✉✐s❛✱ ❡st✉❞❡✐ ❡ ❛ss✐♠✐❧❡✐ ♥♦✈♦s ❝♦♥❝❡✐t♦s✱ ❞❡s❡♥✈♦❧✈✐ ♦s ♠❡✉s r❛❝✐♦❝í♥✐♦s t❡♥t❛♥❞♦ r❡s♦❧✈❡r ✉♠ ♣r♦❜❧❡♠❛ ❞❡t❡r♠✐♥❛❞♦ ❡ ❛ss✐♠ ❢♦✐ s✉r❣✐♥❞♦ ❡st❛ t❡s❡✳ ❆♦ ♠❡s♠♦ t❡♠♣♦ ❡♠ q✉❡ ✜③ t✉❞♦ ✐st♦✱ r❡❝❡❜✐ ❞♦ Pr♦❢❡ss♦r ❏♦ã♦ ❚✐❛❣♦ ▼❡①✐❛✱ ♠❡✉ s✉♣❡r✈✐s♦r✱ ✉♠❛ ❣r❛♥❞✐♦s❛ ♦r✐❡♥t❛çã♦✱ ♠❛♥✐❢❡st❛❞❛ ♣❡r♠❛♥❡♥t❡♠❡♥t❡ ♣♦r ♥♦✈❛s ❡①♣❧✐❝❛çõ❡s✱ s✉❣❡stõ❡s ❡ ❝rít✐✲ ❝❛s ❡ss❡♥❝✐❛✐s à r❡❛❧✐③❛çã♦ ❞❡st❛ t❡s❡✳ P❛r❛ ❡❧❡✱ ♦ ♠❡✉ ✐♥✜♥✐t♦ ❛❣r❛❞❡❝✐♠❡♥t♦✱ ♥ã♦ só ♣❡❧♦ s❡✉ ♣❡r♠❛♥❡♥t❡ ❡ ❛t❡♥❝✐♦s♦ ❛❝♦♠♣❛♥❤❛♠❡♥t♦✱ ♠❛s t❛♠❜é♠ ♣❡❧❛ ❞❡❞✐❝❛çã♦ ❡ ❡♥❝♦r❛❥❛♠❡♥t♦ ❞❡♠♦♥str❛❞♦s ♥♦s ♠♦♠❡♥t♦s ❡♠ q✉❡ ❞✐ss♦ ♣r❡❝✐s❡✐✳

❆ ❢❛♠í❧✐❛ é ✉♠ ♣✐❧❛r ❡ss❡♥❝✐❛❧ ♥❛ ♥♦ss❛ ✈✐❞❛✳ ❆❝♦♠♣❛♥❤❛r❛♠✲s❡ s❡♠♣r❡ ❞✉r❛♥t❡ ❡st❡ ❧♦♥❣♦ ♣❡r❝✉rs♦✱ s❛❜❡♥❞♦ ❡s❝✉t❛r✲♠❡ ❡ ❛❝♦♥s❡❧❤❛r✲♠❡ ♥♦s ♠♦♠❡♥t♦s ♠❛✐s ❞✐❢í❝❡✐s✳ ❆ss✐♠ é ❝♦♠ ❆♠♦r✱ ❝❛r✐♥❤♦ ❡ ❡st✐♠❛ q✉❡ ❛❣r❛❞❡ç♦ ❡ r❡❝♦♥❤❡ç♦ t♦❞♦ ♦ ❛♣♦✐♦✱ ❝♦♠♣r❡❡♥sã♦ ❡ ♣❛❝✐ê♥❝✐❛ q✉❡ r❡❝❡❜✐ ❞♦s ♠❡✉s ♣❛✐s✱ ❞♦ ♠❡✉ ♠❛r✐❞♦ ❆r♠❛♥❞♦ ❡ ❞♦ ♠❡✉ ✜❧❤♦ ❉✐❡❣♦✱ q✉❡ ❝♦♠❡ç♦✉ ❛ ♦✉✈✐r ❢❛❧❛r ❞❡st❛s ❝♦✐s❛s ❛✐♥❞❛ ❡r❛ ✉♠ ♣❡q✉❡♥✐♥♦ ❡♠❜r✐ã♦ ❡ t❡♠ t✐❞♦✱ ❞❡s❞❡ ❡♥tã♦✱ ✉♠❛ ♠ã❡ ❝♦♠ ✉♠❛ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡ ♠✉✐t♦ ❧✐♠✐t❛❞❛✳ ➱ ❝♦♠ ♠✉✐t❛ ❣r❛t✐❞ã♦ q✉❡ r❡❛❧ç♦ ♦ ♣r♦❢✉♥❞♦ ❛❣r❛❞❡❝✐♠❡♥t♦ à ♠✐♥❤❛ ♠ã❡✱ ♣♦r t❡r s✐❞♦ ♠ã❡ ✧❞✉❛s ✈❡③❡s✧✱ ❛♦ ❧♦♥❣♦ ❞❡ t♦❞♦ ❡st❡ ♣❡rí♦❞♦✳ ●♦st❛r✐❛ ❛✐♥❞❛ ❞❡ ♠❡♥❝✐♦♥❛r t♦❞♦ ♦ ❡♥❝♦r❛❥❛♠❡♥t♦ ❡ ♠♦t✐✈❛çã♦ q✉❡ s❡♠♣r❡ r❡❝❡❜✐ ❞♦s ♠❡✉s ❛✈ós ❡ ♦ ❛♣♦✐♦ ❞❛ ♠✐♥❤❛ ✐r♠ã ■♥ês✳

❆❣r❛❞❡ç♦ t❛♠❜é♠ ❛ t♦❞♦s ♦s ♠❡✉s ❛♠✐❣♦s q✉❡ ♠❡ ❞❡r❛♠ ❢♦rç❛ ❡ s❡♠♣r❡ ♠❡ ❡♥❝♦r❛❥❛r❛♠ ♣❛r❛ s❡❣✉✐r ❡♠ ❢r❡♥t❡✳ ❊♠ ❡s♣❡❝✐❛❧✱ à ♠✐♥❤❛ ❛♠✐❣❛ ❈é❧✐❛ ◆✉♥❡s✱ q✉❡ ♠❡ ❛❥✉❞♦✉ s❡♠♣r❡ ♦❢❡r❡❝❡♥❞♦ ❛ s✉❛ ❣r❛♥❞❡ ❛♠✐③❛❞❡✱ s♦❜r❡t✉❞♦ ♦✉✈✐♥❞♦✲♠❡ s❡♠♣r❡ q✉❡ ♣r❡❝✐s❡✐✳ ◆ã♦ ♣♦ss♦ ❡sq✉❡❝❡r t❛♠❜é♠ t♦❞❛s ❛s ✐♥❢♦r♠❛çõ❡s q✉❡ ❡❧❛✱ ❛ ❙❛♥❞r❛ ❡ ♦ ❉❛r✐♦ ♠❡ ❞❡r❛♠ s♦❜r❡ ♦ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞♦ ▲❛t❡①✳

◗✉❡r♦ ❛✐♥❞❛ ❞❡❞✐❝❛r ♦s ♠❡✉s ❛❣r❛❞❡❝✐♠❡♥t♦s s✐♥❝❡r♦s às s❡❣✉✐♥t❡s ♣❡ss♦❛s✿

• ❆♦ ♣r♦❢❡ss♦r ❙t❛♥✐s❧❛✇ ▼❡❥③❛ ♣❡❧❛s ❝rít✐❝❛s ❝♦♥str✉t✐✈❛s✱ s✉❣❡stõ❡s ❡ ❡①♣❧✐❝❛çõ❡s❀

• ❆♦ Pr♦❢❡ss♦r ❚❛❞❡✉s③ ❈❛❧✐♥s❦✐ ♣❡❧❛s s✉❛s ✐♠♣♦rt❛♥t❡s s✉❣❡stõ❡s ❡ ❝♦♠❡♥tár✐♦s❀

• ➚s ♣❡ss♦❛s ❞♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❈❡r❡❛✐s ❞❛ ❊st❛çã♦ ◆❛❝✐♦♥❛❧ ❞❡ ▼❡❧❤♦r❛♠❡♥t♦ ❞❡ P❧❛♥t❛s✱ ♥♦♠❡❛❞❛♠❡♥t❡ ❛♦ ❙❡♥❤♦r ❊♥❣❡♥❤❡✐r♦ ❇❡♠✈✐♥❞♦ ▼❛çãs ❡ ❛♦ ❙❡♥❤♦r ❊♥❣❡♥✲ ❤❡✐r♦ ❏♦ã♦ ❈♦❝♦✱ ♣❡❧❛ r❡❝♦❧❤❛✱ ❡♥✈✐♦ ❡ ❡①♣❧✐❝❛çã♦ ❞♦s ❞❛❞♦s ✉t✐❧✐③❛❞♦s ♥❛ ❛♣❧✐❝❛çã♦ ♣rát✐❝❛ ❞❡st❛ t❡s❡❀

P♦r ú❧t✐♠♦ ❞❡✐①♦ t❛♠❜é♠ ♦ ♠❡✉ ❛❣r❛❞❡❝✐♠❡♥t♦ às ❡♥t✐❞❛❞❡s q✉❡ ❝♦♥tr✐❜✉ír❛♠ ♣❛r❛ ❛ ❛tr✐❜✉✐çã♦ ❞❛ ❜♦❧s❛ ❞❡ ❡st✉❞♦ q✉❡ ♠❡ ♣❡r♠✐t✐✉ ❞❡❞✐❝❛r✲♠❡ ✐♥t❡✐r❛♠❡♥t❡ ❛ ❡st❡ tr❛❜❛❧❤♦✳

❘❡s✉♠♦

❆ ❆♥á❧✐s❡ ❈♦♥❥✉♥t❛ ❞❡ ❘❡❣r❡ssõ❡s✱ ❆❈❘✱ é ✉♠❛ té❝♥✐❝❛ ❝♦♥❤❡❝✐❞❛ ♣❡❧❛ s✉❛ ✉t✐❧✐③❛çã♦ ♥❛ ❝♦♠♣❛r❛çã♦ ❡ s❡❧❡❝çã♦ ❞❡ ❝✉❧t✐✈❛r❡s✳ ❆ s✉❛ ❛♣❧✐❝❛çã♦ ❡st❛✈❛ ❣❡r❛❧♠❡♥t❡ ❝♦♥❞✐❝✐♦♥❛❞❛ ❛ ❡♥✲ s❛✐♦s r❡❛❧✐③❛❞♦s ♥✉♠ ♥ú♠❡r♦ r❡❞✉③✐❞♦ ❞❡ ❛♥♦s✱ ♣❛r❛ ✉♠ ❝♦♥❥✉♥t♦ ✜①♦ ❞❡ ❝✉❧t✐✈❛r❡s✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ✈❛♠♦s ❡st✉❞❛r ❛ ❡①t❡♥sã♦ ❞♦ â♠❜✐t♦ ❞❡ ❛♣❧✐❝❛çã♦ ❞❡st❛ té❝♥✐❝❛ ❛ ♣❧❛♥♦s ❞❡ ♠❡❧✲ ❤♦r❛♠❡♥t♦✳

❖s ❡♥s❛✐♦s ❛♥❛❧✐s❛❞♦s ❛tr❛✈és ❞❛ ❆❈❘ ❡♥❝♦♥tr❛♠✲s❡ ❞✐✈✐❞✐❞♦s ❡♠ ❜❧♦❝♦s✳ ❆ ♣r♦❞✉t✐✈✐❞❛❞❡ ❞❡ ❝❛❞❛ ❜❧♦❝♦ é ♠❡❞✐❞❛ ♣❡❧♦ r❡s♣❡❝t✐✈♦ í♥❞✐❝❡ ❛♠❜✐❡♥t❛❧✳ ❆ té❝♥✐❝❛ ❞❛ ❆❈❘✱ ❝♦♠♦ ♦ s❡✉ ♣ró♣r✐♦ ♥♦♠❡ ✐♥❞✐❝❛✱ ❝♦♥s✐st❡ ♥♦ ❛❥✉st❛♠❡♥t♦ ❞❡ r❡❣r❡ssõ❡s ❧✐♥❡❛r❡s ❞♦ r❡♥❞✐♠❡♥t♦ ❞❡ ❝❛❞❛ ❝✉❧t✐✈❛r ♥♦ r❡s♣❡❝t✐✈♦ í♥❞✐❝❡ ❛♠❜✐❡♥t❛❧✳

◆✉♠❛ ♣r✐♠❡✐r❛ ♣❛rt❡✱ ❛♣r❡s❡♥t❛♠♦s ❛s té❝♥✐❝❛s ❡st❛tíst✐❝❛s q✉❡ s❡rã♦ ✉t✐❧✐③❛❞❛s ♣♦st❡r✐♦r✲ ♠❡♥t❡ ♥❛ ❛♥á❧✐s❡ ❞✉♠ ♣❧❛♥♦ ❞❡ ♠❡❧❤♦r❛♠❡♥t♦ ❝♦♥❝r❡t♦✳ ▼♦str❛r❡♠♦s ♥♦♠❡❛❞❛♠❡♥t❡✱ ❝♦♠♦ r❡❛❧✐③❛r ♦s ❛❥✉st❛♠❡♥t♦s ❞❛s r❡❣r❡ssõ❡s ❧✐♥❡❛r❡s ❡ ❝♦♠♦ ♣r♦❝❡❞❡r à ❝♦♠♣❛r❛çã♦ ❡ s❡❧❡❝çã♦ ❞♦s ❝✉❧t✐✈❛r❡s✳

◆❛ s❡❣✉♥❞❛ ♣❛rt❡ ♦ ♥♦ss♦ tr❛❜❛❧❤♦ ♠♦str❛rá✱ r❡✈❡♥❞♦✲s❡ ♥♦ P❧❛♥♦ ❞❡ ▼❡❧❤♦r❛♠❡♥t♦ ❞❡ ❚r✐❣♦ ▼♦❧❡ ❡♠ P♦rt✉❣❛❧ ✭✶✾✽✻ ✲ ✷✵✵✵✮✱ ❝♦♠♦ ✉t✐❧✐③❛r ❛ ❆❈❘ ❡♠ ♣❧❛♥♦s ❞❡ ♠❡❧❤♦r❛♠❡♥t♦✳

❆♣r❡s❡♥t❛r❡♠♦s ❛✐♥❞❛ ✉♠ ♠♦❞❡❧♦ ♣❛r❛ ♦s í♥❞✐❝❡s ❛♠❜✐❡♥t❛✐s✱ ✉s❛♥❞♦ ✈❛r✐á✈❡✐s ❞✉♠♠② ❛ss♦✲ ❝✐❛❞❛s ❛ ❛♥♦s✱ ❧♦❝❛✐s ❡ ❝✉❧t✐✈❛r❡s✳ ❖s ❝♦❡✜❝✐❡♥t❡s ❛❥✉st❛❞♦s ♣❛r❛ ♦s ❛♥♦s ❢♦r❛♠ ✉s❛❞♦s ♣❛r❛ ❡①♣r❡ss❛r✱ ♥♦ ❝❛s♦ ❞♦ Pr♦❣r❛♠❛ ❞❡ ▼❡❧❤♦r❛♠❡♥t♦ ❞♦ ❚r✐❣♦ ▼♦❧❡ ❡♠ P♦rt✉❣❛❧✱ ♦s ❡❢❡✐t♦s ❛tr✐❜✉í✈❡✐s ❛♦ ❢❛❝t♦r ❛♥♦✳

❖s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♥♦ ❝❛s♦ P♦rt✉❣✉ês✱ ✐♥❞✐❝❛♠ ❝❧❛r❛♠❡♥t❡ ❛ ✉t✐❧✐❞❛❞❡ ❞❛ té❝♥✐❝❛ ❞❛ ❆❈❘ ♥♦ ❛❝♦♠♣❛♥❤❛♠❡♥t♦ ❞❡ ♣r♦❣r❛♠❛s ❞❡ ♠❡❧❤♦r❛♠❡♥t♦✱ ♠❛✐s ♣r❡❝✐s❛♠❡♥t❡✱ ♥❛ t♦♠❛❞❛ ❞❡ ❞❡❝✐sã♦ r❡❧❛t✐✈❛ ❛♦s ❝✉❧t✐✈❛r❡s q✉❡ ❞❡✈❡♠ ♣❡r♠❛♥❡❝❡r ♥♦ ♣❧❛♥♦ ❞❡ ♠❡❧❤♦r❛♠❡♥t♦ ❞❡ ✉♠ ❛♥♦ ♣❛r❛ ♦ ♦✉tr♦✳

❆❜str❛❝t

❏♦✐♥t ❘❡❣r❡ss✐♦♥ ❆♥❛❧②s✐s ✐s ❛ ✇❡❧❧ ❦♥♦✇♥ t❡❝❤♥✐q✉❡ ❢♦r ❝✉❧t✐✈❛r ❝♦♠♣❛r✐s♦♥ ❛♥❞ s❡❧❡❝t✐♦♥✳ ❯s✉❛❧❧②✱ ❛ s♠❛❧❧ ♥✉♠❜❡r ♦❢ ②❡❛rs ❛♥❞ ❛ ❣✐✈❡♥ ❧✐st ♦❢ ❝✉❧t✐✈❛rs ❛r❡ ❝♦♥s✐❞❡r❡❞✱ ✇❤❡♥ ❛♣♣❧②✐♥❣ t❤❡ t❡❝❤♥✐q✉❡✳ ❲❡ ♥♦✇ ❞✐s❝✉ss t❤❡ ❡①t❡♥s✐♦♥ ♦❢ t❤❡ t❡❝❤♥✐q✉❡ t♦ ♣❧❛♥t ❜r❡❡❞✐♥❣ ♣r♦❣r❛♠s✳ ❚❤❡ ✜❡❧❞ tr✐❛❧s ❛♥❛❧②③❡❞ t❤r♦✉❣❤ ❏❘❆ ❛r❡ ❞✐✈✐❞❡❞ ✐♥ ❜❧♦❝❦s✳ ❚❤❡ ♣r♦❞✉❝t✐✈✐t② ♦❢ ❡❛❝❤ ❜❧♦❝❦ ✐s ♠❡❛s✉r❡❞ ❜② ✐t✬s ❡♥✈✐r♦♥♠❡♥t❛❧ ✐♥❞❡①✳ P❡r ❝✉❧t✐✈❛r✱ ❛ ❧✐♥❡❛r r❡❣r❡ss✐♦♥ ♦❢ t❤❡ ②✐❡❧❞ ♦♥ ❡♥✈✐r♦♥♠❡♥t❛❧ ✐♥❞❡① ✐s ❛❞❥✉st❡❞✱ ✇❤✐❝❤ ❣❛✈❡ t❤❡ t❡❝❤♥✐q✉❡ ✐t✬s ♥❛♠❡✳

■♥ ❛ ✜rst ♣❛rt✱ t❤❡ r❡q✉✐r❡❞ st❛t✐st✐❝❛❧ t❡❝❤♥✐q✉❡s ❛r❡ ♣r❡s❡♥t❡❞✳ ◆❛♠❡❧②✱ ✐t ✐s s❤♦✇♥✱ ❤♦✇ t♦ ❛❞❥✉st t❤❡ ❧✐♥❡❛r r❡❣r❡ss✐♦♥s ❛♥❞ ❤♦✇ t♦ ❝♦♠♣❛r❡ ❝✉❧t✐✈❛rs✳

◆❡①t❧②✱ t❤❡ ❛♣♣❧✐❝❛t✐♦♥ ♦❢ ❏❘❆ t♦ ♣❧❛♥t ❜r❡❡❞✐♥❣ ♣r♦❣r❛♠s ✐s ♣❡r❢♦r♠❡❞✳ ❚❤✐s ❛♣♣❧✐❝❛t✐♦♥ ✐s ❝❛rr✐❡❞ ♦✉t ✇✐t❤ ❡♠♣❤❛s✐s ✐♥ t❤❡ P♦rt✉❣✉❡s❡ ❲❤❡❛t ❇r❡❡❞✐♥❣ Pr♦❣r❛♠ ✭✶✾✽✻ ✲ ✷✵✵✵✮✳ ■t ✐s s❤♦✇♥ ❤♦✇ t♦ ❛❞❥✉st ❛ ♠♦❞❡❧ ❢♦r ❡♥✈✐r♦♥♠❡♥t❛❧ ✐♥❞❡①❡s ✇✐t❤ ❞✉♠♠② ✈❛r✐❛❜❧❡s ❛ss♦✲ ❝✐❛t❡❞ t♦ ②❡❛rs✱ ❧♦❝❛t✐♦♥s ❛♥❞ ❝✉❧t✐✈❛rs✳ ❚❤❡ ②❡❛r ❝♦❡✣❝✐❡♥ts ✇❡r❡ ✉s❡❞ t♦ ❡①♣r❡ss✱ ❢♦r t❤❡ P♦rt✉❣✉❡s❡ ❲❤❡❛t ❇r❡❡❞✐♥❣ Pr♦❣r❛♠✱ ②❡❛r ❡✛❡❝ts✳

❚❤❡ r❡s✉❧ts ♦❜t❛✐♥❡❞ ✐♥ t❤❡ st✉❞✐❡❞ ❝❛s❡ ❝❧❡❛r❧② ✐♥❞✐❝❛t❡ t❤❡ ✉s❡❢✉❧♥❡ss ♦❢ ❏❘❆✳ ◆❛♠❡❧②✱ t❤❡ t❡❝❤♥✐q✉❡ ✐s ✉s❡❢✉❧ ✐♥ ❞❡❝✐❞✐♥❣ ✇❤✐❝❤ ♦❢ t❤❡ ❝✉❧t✐✈❛rs ✉s❡❞ s❤♦✉❧❞ ❜❡ ❦❡♣t ❢♦r t❤❡ ♥❡①t ②❡❛r✳

▲✐st❛ ❞❡ sí♠❜♦❧♦s ❡ s✐❣❧❛s

ACR ❆♥á❧✐s❡ ❝♦♥❥✉♥t❛ ❞❡ r❡❣r❡ssã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶ L2 ■♥❞✐❝❡s L2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶

θb ✈❡❝t♦r ❞♦ ♣❛râ♠❡tr♦ ❞❡ ❡str✉t✉r❛ ❝♦♠ b ❝♦♠♣♦♥❡♥t❡s ✳ ✳ ✳ ✻

X(θb) ♠❛tr✐③ ❞♦ ♠♦❞❡❧♦ q✉❡ ❞❡♣❡♥❞❡ ❞♦ ✈❡❝t♦r ❞❡ ❡str✉t✉r❛ θb ✻

♥ × ❦ ♥ ❧✐♥❤❛s ❡ ❦ ❝♦❧✉♥❛s ♥✉♠❛ ♠❛tr✐③ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻

γ_k ✈❡❝t♦r ❞♦s ❝♦❡✜❝✐❡♥t❡s ♣❛r❛ ❛s r❡❣r❡ssõ❡s ❧✐♥❡❛r❡s ❝♦♠k❝♦♠✲

♣♦♥❡♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻

y_n ✈❡❝t♦r ❞❡ ♦❜s❡r✈❛çõ❡s ❞❛ ✈❛r✐á✈❡❧ ❞❡♣❡♥❞❡♥t❡ ❝♦♠ ♥ ❝♦♠♣♦✲

♥❡♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻

E(y_n) ✈❛❧♦r ❡s♣❡r❛❞♦ ❞♦ ✈❡❝t♦r y_n ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻

R[X(θo_b)] ❡s♣❛ç♦ ✐♠❛❣❡♠ ❞❛ ♠❛tr✐③ X(θo_b) ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ S(γ_k,θb) ❢✉♥çã♦ ♦❜❥❡❝t✐✈♦ ❛ ♠✐♥✐♠✐③❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳✻ θ1,b ✈❡❝t♦r ❞❡ ❡str✉t✉r❛ ✐♥✐❝✐❛❧ ❝♦♠ ❜ ❝♦♠♣♦♥❡♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳✻

S(γk|θ1,b) ❢✉♥çã♦ ♦❜❥❡❝t✐✈♦ ❛ ♠✐♥✐♠✐③❛r ❡♠ ♦r❞❡♠ ❛ γk ❞❛❞♦ θ1,b ✳ ✳ ✻ ˜

γ₁,k ❡st✐♠❛❞♦r ♣❛r❛ γk ♦❜t✐❞♦ ♥❛ ♣r✐♠❡✐r❛ ✐t❡r❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻

ℵ ❞❡✜♥❡ ❛ ❢❛♠í❧✐❛ ❞❛s ♠❛tr✐③❡s ❞♦ ♠♦❞❡❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼

ς r❡❧❛çã♦ ❞❡ ❡q✉✐✈❛❧ê♥❝✐❛ ❡♥tr❡ ♠❛tr✐③❡s ❞♦ ♠♦❞❡❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ Γ ❡s♣❛ç♦ ♣❛r❛♠étr✐❝♦ ❞♦s ✈❡❝t♦r❡s ❞❡ ❡str✉t✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ⊳vb ♠í♥✐♠♦ ❞❛s ❝♦♠♣♦♥❡♥t❡s ❞♦ ✈❡❝t♦r vb ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳✼

⊲vb ♠á①✐♠♦ ❞❛s ❝♦♠♣♦♥❡♥t❡s ❞♦ ✈❡❝t♦r vb ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ˜

θ1,b ❡st✐♠❛❞♦r ♣❛r❛ θb ♦❜t✐❞♦ ♥❛ ♣r✐♠❡✐r❛ ✐t❡r❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ Ω⊥ _{❝♦♠♣❧❡♠❡♥t♦ ♦rt♦❣♦♥❛❧ ❞♦ ❡s♣❛ç♦ Ω ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳✼}

y_Ω⊥ ♣r♦❥❡❝çã♦ ♦rt♦❣♦♥❛❧ ❞❡ y s♦❜r❡ Ω⊥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼

kak ♥♦r♠❛ ❞♦ ✈❡❝t♦r a ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼

J ♥ú♠❡r♦ ❞❡ ❝✉❧t✐✈❛r❡s ✉t✐❧✐③❛❞♦s ♥♦ ❡st✉❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽

yj,nj ✈❡❝t♦r ❞♦s r❡♥❞✐♠❡♥t♦s ♣❛r❛ ♦j✲és✐♠♦ ❝✉❧t✐✈❛r ❝♦♠ nj ❝♦♠✲

♣♦♥❡♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽

n ♥ú♠❡r♦ t♦t❛❧ ❞❡ ♦❜s❡r✈❛çõ❡s ♥♦ ♠♦❞❡❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽

D(X1, ...,XJ) ♠❛tr✐③ ❞✐❛❣♦♥❛❧ ♣♦r ❜❧♦❝♦s ❝♦♠ ❜❧♦❝♦s ♣r✐♥❝✐♣❛✐s✱X1, ...,XJ

✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽

1nj ✈❡❝t♦r ❝♦♠ nj ❝♦♠♣♦♥❡♥t❡s ✐❣✉❛✐s ❛ ✉♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽

nj ♥ú♠❡r♦ ❞❡ ♦❜s❡r✈❛çõ❡s ♣❛r❛ ♦ j✲és✐♠♦ ❝✉❧t✐✈❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽

xj,nj ✈❡❝t♦r ❝♦♠ nj ❝♦♠♣♦♥❡♥t❡s✱ s❡♥❞♦ ❛i✲és✐♠❛ ❝♦♠♣♦♥❡♥t❡ ♦

í♥❞✐❝❡ ❛♠❜✐❡♥t❛❧ ❞♦ ❜❧♦❝♦ ♦♥❞❡ s❡ ♦❜t❡✈❡ ❛ ✐✲és✐♠❛ ♣r♦❞✉çã♦ ❞♦ ❥✲és✐♠♦ ❝✉❧t✐✈❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽

γ_2J ✈❡❝t♦r ❞♦s ❝♦❡✜❝✐❡♥t❡s ♣❛r❛ ❛s r❡❣r❡ssõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽

pi,j ♣❡s♦ ❛tr✐❜✉í❞♦ ❛♦ j✲és✐♠♦ ❝✉❧t✐✈❛r ♥♦ i✲és✐♠♦ ❜❧♦❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✽

b ♥ú♠❡r♦ ❞❡ ♣❛r❡s ✭❧♦❝❛❧✱ ❛♥♦✮ ♦✉ í♥❞✐❝❡s ❛♠❜✐❡♥t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✽ xi í♥❞✐❝❡ ❛♠❜✐❡♥t❛❧ ❞♦ ✐✲és✐♠♦ ❜❧♦❝♦✱ ♣❛r ✭❧♦❝❛❧✱❛♥♦✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽

xb ✈❡❝t♦r ❞❡ ❡str✉t✉r❛ ❝✉❥❛s ❝♦♠♣♦♥❡♥t❡s sã♦ ♦sb í♥❞✐❝❡s ❛♠✲

❜✐❡♥t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽

yi,j r❡♥❞✐♠❡♥t♦ ❞♦j✲és✐♠♦ ❝✉❧t✐✈❛r ♥♦ i✲és✐♠♦ ❜❧♦❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽

xi,0 ✈❛❧♦r ✐♥✐❝✐❛❧ ♣❛r❛ ♦ í♥❞✐❝❡ ❛♠❜✐❡♥t❛❧ ❞♦ i✲és✐♠♦ ❜❧♦❝♦ ✳ ✳ ✳ ✳ ✾

(αj, βj) ♦r❞❡♥❛❞❛ ♥❛ ♦r✐❣❡♠ ❡ ❝♦❡✜❝✐❡♥t❡ ❛♥❣✉❧❛r ❞❛ r❡❝t❛ ❞❡ r❡✲

❣r❡ssã♦ ❛ ❛❥✉st❛r ♣❛r❛ ♦ j✲és✐♠♦ ❝✉❧t✐✈❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ S1(αJ,βJ) ❢✉♥çã♦ ♦❜❥❡❝t✐✈♦ ❛ ♠✐♥✐♠✐③❛r ❡♠ ♦r❞❡♠ ❛ αJ ❡ βJ ♥❛

♣r✐♠❡✐r❛ ✐t❡r❛çã♦ ❞♦ ❛❧❣♦r✐t♠♦ ❩✐❣✲❩❛❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾

(˜αj,1,β˜j,1) ❡st✐♠❛❞♦r❡s ❞♦s ♠í♥✐♠♦s q✉❛❞r❛❞♦s ♣❛r❛(αj, βj)♦❜t✐❞♦s ♥❛

♣r✐♠❡✐r❛ ✐t❡r❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳✾

S1(xb) ❢✉♥çã♦ ❛ ♠✐♥✐♠✐③❛r ❡♠ ♦r❞❡♠ ❛ xb ♥❛ ♣r✐♠❡✐r❛ ✐t❡r❛çã♦ ❞♦ ❛❧❣♦r✐t♠♦ ❩✐❣✲❩❛❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾

min[x1,o, ..., xb,o] r❡♣r❡s❡♥t❛ ♦ ♠í♥✐♠♦ ❞♦s ❡❧❡♠❡♥t♦s ❞♦ ❝♦♥❥✉♥t♦ ❬ ❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳✾

max[x1,o, ..., xb,o] r❡♣r❡s❡♥t❛ ♦ ♠á①✐♠♦ ❞♦s ❡❧❡♠❡♥t♦s ❞♦ ❝♦♥❥✉♥t♦ ❬ ❪ ✳ ✳ ✳ ✳ ✳ ✳ ✾ IRb×IRJ ×IRJ ❡s♣❛ç♦ ♦❜t✐❞♦ ♣❡❧♦ ♣r♦❞✉t♦ ❝❛rt❡s✐❛♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾

❛ ϕ ❜ ❛ é ϕ ❡q✉✐✈❛❧❡♥t❡ ❛ ❜ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳✾

R(1b) ❡s♣❛ç♦ ✐♠❛❣❡♠ ❞❛s ♠❛tr✐③❡s ❝♦❧✉♥❛ ❝♦♠ t♦❞❛s ❛s ❝♦♠♣♦✲

♥❡♥t❡s ✐❣✉❛✐s ❛ ✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ■♥t✭❛✮ ♣❛rt❡ ✐♥t❡✐r❛ ❞❡ ❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸

grad(S1) ❣r❛❞✐❡♥t❡ ❞❛ ❢✉♥çã♦ S1 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹

Hess(S1) ♠❛tr✐③ ❤❡ss✐❛♥❛ ❞❡S1 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺

Uj,l(u, v) ❢✉♥çã♦ ♦❜❥❡❝t✐✈♦ ❛ss♦❝✐❛❞❛ ❛♦j✲és✐♠♦ ❝✉❧t✐✈❛r ❡l✲és✐♠♦ ❛♥♦

✶✾

˜

S ❙♦♠❛ ❞❛s s♦♠❛s ❞♦s q✉❛❞r❛❞♦s ❞♦s r❡sí❞✉♦s ❞❛s r❡❣r❡ssõ❡s

❝♦rr❡s♣♦♥❞❡♥t❡s à ú❧t✐♠❛ ✐t❡r❛çã♦ ❞♦ ❛❧❣♦r✐t♠♦ ❩✐❣✲❩❛❣ ✷✵

x∼N[a,B] ♦ ✈❡❝t♦r ❛❧❡❛tór✐♦xt❡♠ ❞✐str✐❜✉✐çã♦ ◆♦r♠❛❧ ❝♦♠ ✈❛❧♦r ♠é✲

❞✐♦ a ❡ ♠❛tr✐③ ❞❡ ❝♦✈❛r✐â♥❝✐❛ B ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵

g ♥ú♠❡r♦ t♦t❛❧ ❞❡ ❣r❛✉s ❞❡ ❧✐❜❡r❞❛❞❡ ❛ss♦❝✐❛❞♦s ❛S˜ ✳ ✳ ✳ ✳ ✳ ✷✵ bj ♥ú♠❡r♦ ❞❡ ❜❧♦❝♦s ❡♠ q✉❡ ♦ ❝✉❧t✐✈❛r j ❡stá ♣r❡s❡♥t❡ ✳ ✳ ✳ ✳ ✳✷✵

h ♥ú♠❡r♦ ❞❡ ❛♥♦s ❝♦♥s✐❞❡r❛❞♦s ♥♦ ♣❧❛♥♦ ❞❡ ♠❡❧❤♦r❛♠❡♥t♦ ✷✶

(˜αj,l,β˜j,l) ❝♦❡✜❝✐❡♥t❡s ❞❡ r❡❣r❡ssã♦ ❛❥✉st❛❞♦s ♣❛r❛ ♦ j✲és✐♠♦ ❝✉❧t✐✈❛r

♥♦l✲és✐♠♦ ❛♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶

H₀,j,j′(1, vo) ❤✐♣ót❡s❡ ♥✉❧❛ r❡❧❛t✐✈❛ ❛♦s j✲és✐♠♦ ❡ j

′

✲és✐♠♦ ❝✉❧t✐✈❛r❡s ❡ à ❢✉♥çã♦ U(1, vo) ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸

t_j,j′(1, v_o) ✈❛❧♦r ❞❛ ❡st❛tíst✐❝❛ ❞♦ t❡st❡t♣❛r❛ ❝♦♠♣❛r❛çã♦ ❞♦s ❝✉❧t✐✈❛r❡s

j ❡ j′ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ F1−α,v1,v2 ✈❛❧♦r ❝rít✐❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡ à ❞✐str✐❜✉✐çã♦ ❋ ❞❡ ❙♥❡❞❝♦r ❝❡♥✲

tr❛❧✱ ❝♦♠ v1 ❡ v2 ❣r❛✉s ❞❡ ❧✐❜❡r❞❛❞❡✱ ♣❛r❛ ❛ ♦ ♥í✈❡❧ ❞❡ s✐❣✲ ♥✐✜❝â♥❝✐❛ α ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸

Dj ❝♦♥❥✉♥t♦ ❞♦s í♥❞✐❝❡s ❞♦s ❛♥♦s ❡♠ q✉❡ ♦ j✲és✐♠♦ ❝✉❧t✐✈❛r ❢♦✐

✉t✐❧✐③❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹

A′ tr❛♥s♣♦st❛ ❞❛ ♠❛tr✐③A ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ diag(r1, ..., rm) ♠❛tr✐③ ❞✐❛❣♦♥❛❧ ❝♦♠ ❡❧❡♠❡♥t♦s ♣r✐♥❝✐♣❛✐sr1, ..., rm ✳ ✳ ✳ ✳ ✳ ✷✹

Car(A) ❝❛r❛❝t❡ríst✐❝❛ ❞❛ ♠❛tr✐③A ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹

sul s♦♠❛ ❞♦s q✉❛❞r❛❞♦s ❞♦s ❞❡s✈✐♦s ♣❛r❛ ❛ ♠é❞✐❛ ❞♦s í♥❞✐❝❡s

❛♠❜✐❡♥t❛✐s ❛❥✉st❛❞♦s ♥♦ ❛♥♦ ❝♦♠ í♥❞✐❝❡ ul ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ A⊗B ♣r♦❞✉t♦ ❞❡ ❑r♦♥❡❝❦❡r ❞❡ A♣♦r B ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼

V ar(U) ✈❛r✐â♥❝✐❛ ❞❛ ✈❛r✐á✈❡❧ ❯ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳✷✼ Cov( ˜U) ♠❛tr✐③ ❞❡ ❝♦✈❛r✐â♥❝✐❛ ❞♦ ✈❡❝t♦r U˜ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼

Ci ❝♦♥❥✉♥t♦ ❞♦s í♥❞✐❝❡s ❞♦s ❝✉❧t✐✈❛r❡s ♣r❡s❡♥t❡s ♥♦ i✲és✐♠♦

❜❧♦❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽

l(γ_2J,θb, σ2_{) ❧♦❣❛r✐t♠♦ ❞❛ ❢✉♥çã♦ ❞❡ ♠á①✐♠❛ ✈❡r♦s✐♠✐❧❤❛♥ç❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾}

ˆ

σ2 _{❡st✐♠❛❞♦r ❞❡ ♠á①✐♠❛ ✈❡r♦s✐♠✐❧❤❛♥ç❛ ♣❛r❛σ}2 _{✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾}

(γˆ₂J,θbˆ) ❡st✐♠❛❞♦r❡s ❞❡ ♠á①✐♠❛ ✈❡r♦s✐♠✐❧❤❛♥ç❛ ♣❛r❛ ♦ ♣❛r (γ₂J,θb).... ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾

w ❡s♣❛ç♦ ♣❛r❛♠étr✐❝♦ ❛ss♦❝✐❛❞♦ ❛ Ho ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ Ω ❡s♣❛ç♦ ♣❛r❛♠étr✐❝♦ t♦t❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ L(αJ,βJ,θb, σ2)❢✉♥çã♦ ❞❡ ♠á①✐♠❛ ✈❡r♦s✐♠✐❧❤❛♥ç❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾

xg,1−α q✉❛♥t✐❧ ♣❛r❛ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ 1−α ❞❛ ❞✐str✐❜✉✐çã♦ ❞♦ q✉✐✲

q✉❛❞r❛❞♦ ❝♦♠ g ❣r❛✉s ❞❡ ❧✐❜❡r❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻

≈ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ♣r♦❜✭✳✮ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ✭✳✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻

θ_j,j′ ♣♦♥t♦ ❞❡ ✐♥t❡rs❡❝çã♦ ❡♥tr❡ ❛s r❡❝t❛s ❞❡ r❡❣r❡ssã♦ ❛❥✉st❛❞❛s

❝♦♠ í♥❞✐❝❡s j ❡j′ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵

Vb ✈❡❝t♦r ❞♦s í♥❞✐❝❡s ❛♠❜✐❡♥t❛✐s ♥♦ ♠♦❞❡❧♦ ♣❛r❛ ♦s í♥❞✐❝❡s ❛♠✲

❜✐❡♥t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵

pi ♥ú♠❡r♦ ❞❡ ❝♦❧✉♥❛s ❞❛ ♠❛tr✐③ ❞♦ ♠♦❞❡❧♦ ❛ss♦❝✐❛❞❛s à ✐✲és✐♠❛

✈❛r✐á✈❡❧ ❡①♣❧✐❝❛t✐✈❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵

X ♠❛tr✐③ ❞♦ ♠♦❞❡❧♦ ♣❛r❛ ♦s í♥❞✐❝❡s ❛♠❜✐❡♥t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶

δh ✈❡❝t♦r ❞♦s ❝♦❡✜❝✐❡♥t❡s ❛ss♦❝✐❛❞♦s à ♠❛tr✐③ ❞♦ ♠♦❞❡❧♦ ✳ ✳ ✽✶

eb ✈❡❝t♦r ❞♦s ❡rr♦s ♥♦ ♠♦❞❡❧♦ ♣❛r❛ ♦s í♥❞✐❝❡s ❛♠❜✐❡♥t❛✐s ✳ ✳ ✽✶

g ♥ú♠❡r♦ ❞❡ ✈❛❧♦r❡s ♣ró♣r✐♦s ♥ã♦ ♥✉❧♦s ❞❛ ♠❛tr✐③X′X ✳ ✳ ✽✶

˜

γ_g ❡st✐♠❛❞♦r ❞❡ ♠í♥✐♠♦s q✉❛❞r❛❞♦s ✉s❛♥❞♦ ❝♦♠♣♦♥❡♥t❡s ♣r✐♥✲

❝✐♣❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷

Scp s♦♠❛ ❞♦s q✉❛❞r❛❞♦s ❞♦s r❡sí❞✉♦s ♣❛r❛ ♦ ♠♦❞❡❧♦ ❡st✐♠❛❞♦

✉s❛♥❞♦ ❝♦♠♣♦♥❡♥t❡s ♣r✐♥❝✐♣❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳✽✷

tr(A) tr❛ç♦ ❞❛ ♠❛tr✐③ A ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ˜

α ♦r❞❡♥❛❞❛ ♥❛ ♦r✐❣❡♠ ❞❛ r❡❝t❛ ❞❡ r❡❣r❡ssã♦ ❧✐♥❡❛r ❛❥✉st❛❞❛ ✽✼

˜

β ❝♦❡✜❝✐❡♥t❡ ❛♥❣✉❧❛r ❞❛ r❡❝t❛ ❞❡ r❡❣r❡ssã♦ ❧✐♥❡❛r ❛❥✉st❛❞❛ ✽✼

❆♦ ❧♦♥❣♦ ❞❡st❡ tr❛❜❛❧❤♦ ♦s ✈❡❝t♦r❡s ❡ ❛s ♠❛tr✐③❡s ❡stã♦ r❡♣r❡s❡♥t❛❞♦s ❛ ♥❡❣r✐t♦✳ ❖ ♥ú♠❡r♦ ❞❡ ❝♦♠♣♦♥❡♥t❡s ❞❡ ✉♠ ✈❡❝t♦r é ♦ ✈❛❧♦r ❛ss✉♠✐❞♦ ♣❡❧♦ í♥❞✐❝❡ ✐♥❢❡r✐♦r ❞♦ ♠❡s♠♦✳ ◗✉❛♥❞♦ ✉♠ ✈❡❝t♦r t❡♠ ❞♦✐s í♥❞✐❝❡s ✐♥❢❡r✐♦r❡s✱ ♦ í♥❞✐❝❡ à ❡sq✉❡r❞❛ ❞❛ ✈ír❣✉❧❛ ✐❞❡♥t✐✜❝❛ ♦ ✈❡❝t♦r ❡ ♦ í♥❞✐❝❡ à ❞✐r❡✐t❛ ❞❛ ✈ír❣✉❧❛ r❡♣r❡s❡♥t❛ ♦ ♥ú♠❡r♦ ❞❡ ❝♦♠♣♦♥❡♥t❡s ❞♦ ♠❡s♠♦✳ ◗✉❛♥❞♦ ✉♠❛ ❝♦♠♣♦♥❡♥t❡ ❞❡ ✉♠ ✈❡❝t♦r t❡♠ ❞♦✐s í♥❞✐❝❡s ✐♥❢❡r✐♦r❡s✱ ♦ q✉❡ ❡stá à ❡sq✉❡r❞❛ ❞❛ ✈ír❣✉❧❛ ♣♦s✐❝✐♦♥❛ ❛ ❝♦♠♣♦♥❡♥t❡ ♥♦ ✈❡❝t♦r ❡♠ q✉❡ s❡ ✐♥s❡r❡ ❡ ♦ í♥❞✐❝❡ à ❞✐r❡✐t❛ ❞❛ ✈ír❣✉❧❛ r❡❢❡r❡✲s❡ ❛♦ ✈❡❝t♦r✳

❈♦♥t❡ú❞♦

▲✐st❛ ❞❡ sí♠❜♦❧♦s ❡ s✐❣❧❛s ■❳

✶ ■♥tr♦❞✉çã♦ ✶

✷ ❆♥á❧✐s❡ ❝♦♥❥✉♥t❛ ❞❡ ❘❡❣r❡ssõ❡s ✺

✷✳✶ ◆♦t❛ ❍✐stór✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✷✳✷ ❆❥✉st❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ ✷✳✷✳✶ ▼í♥✐♠♦s ◗✉❛❞r❛❞♦s ❊str✉t✉r❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ ✷✳✷✳✷ ❆♥á❧✐s❡ ❝♦♥❥✉♥t❛ ❞❡ r❡❣r❡ssã♦ ❡ ❮♥❞✐❝❡s L2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✷✳✸ ❘❡❞❡s ❋r❛❝❝✐♦♥❛❧♠❡♥t❡ ❝♦♠♣❧❡t❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✸ ■♥❢❡rê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✷✳✸✳✶ ❆❧❣✉♠❛s ❝♦♥s✐❞❡r❛çõ❡s ♣r❡❧✐♠✐♥❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✷✳✸✳✷ ❋✉♥çõ❡s ❖❜❥❡❝t✐✈♦ ▲✐♥❡❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✷✳✸✳✸ ❍✐♣ót❡s❡s s♦❜r❡ ✉♠ ❢❛❝t♦r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✷✳✸✳✹ ❍✐♣ót❡s❡s s♦❜r❡ ❞♦✐s ❢❛❝t♦r❡s ❝♦♠ ✐♥t❡r❛❝çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✸✳✺ ❚❡st❡s ❞❡ q✉♦❝✐❡♥t❡ ❞❡ ❱❡r♦s✐♠✐❧❤❛♥ç❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✷✳✸✳✻ ❘❡❣✐õ❡s ❞❡ ❝♦♥✜❛♥ç❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✷✳✹ ❈❧❛ss✐✜❝❛çã♦ ❡ ❙❡❧❡❝çã♦ ❞❡ ❈✉❧t✐✈❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✷✳✹✳✶ ❈❧❛ss✐✜❝❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✷✳✹✳✷ ❙❡❧❡❝çã♦ ♣❡❧♦ ♠ét♦❞♦ ❞♦ ❈♦♥t♦r♥♦ ❙✉♣❡r✐♦r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾

✸ P❧❛♥♦ ❞❡ ▼❡❧❤♦r❛♠❡♥t♦ ❞❡ ❚r✐❣♦ ▼♦❧❡ ✹✼

✸✳✶ ❈♦♥s✐❞❡r❛çõ❡s Pré✈✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✸✳✷ ❮♥❞✐❝❡s ❆♠❜✐❡♥t❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶

❳■❱ ❈♦♥t❡ú❞♦

✸✳✸ ❊st✉❞♦ ❞❛ ❡st❛❜✐❧✐❞❛❞❡ ❞♦s ❝✉❧t✐✈❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✸✳✹ ❈❧❛ss✐✜❝❛çã♦ ❞♦s ❝✉❧t✐✈❛r❡s ♥❛ ❖♣çã♦I ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼

✸✳✺ ❆♥á❧✐s❡ ❞♦ ❈♦♥t♦r♥♦ ❙✉♣❡r✐♦r ♥❛ ♦♣çã♦I ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵

✸✳✻ ❈❧❛ss✐✜❝❛çã♦ ❞♦s ❝✉❧t✐✈❛r❡s ♥❛ ❖♣çã♦II ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹

✸✳✼ ❆♥á❧✐s❡ ❞♦ ❝♦♥t♦r♥♦ s✉♣❡r✐♦r ♥❛ ❖♣çã♦ II ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺

✸✳✽ ❙❡❧❡❝çã♦ ❞❛s ❢✉♥çõ❡s ♦❜❥❡❝t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✸✳✾ ▼á①✐♠♦s ❞❛s ❢✉♥çõ❡s ♦❜❥❡❝t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✸✳✶✵ ❆♥á❧✐s❡ ❞♦s ❣r✉♣♦s ❞❡ ❈✉❧t✐✈❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵

✹ ❮♥❞✐❝❡s ❆♠❜✐❡♥t❛✐s ✼✾

✹✳✶ ❈♦♥s✐❞❡r❛çõ❡s Pré✈✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✹✳✷ ▼♦❞❡❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✹✳✸ ❆❥✉st❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ✹✳✹ ❋✉♥çõ❡s ♦❜❥❡❝t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻

✺ ❈♦♥❝❧✉sõ❡s ❡ ❚r❛❜❛❧❤♦s ❋✉t✉r♦s ✽✾

❆ ✾✶

▲✐st❛ ❞❡ ❚❛❜❡❧❛s

✷✳✶ ●r❡❧❤❛ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❞♦s ❝✉❧t✐✈❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽

✸✳✶ ▲✐st❛ ❞♦s ❝✉❧t✐✈❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✸✳✷ ▲♦❝❛✐s ❡ ❛♥♦s ♦♥❞❡ s❡ r❡❛❧✐③❛r❛♠ ❛s ❡①♣❡r✐ê♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✸✳✸ Pr❡s❡♥ç❛ ❡ ❛✉sê♥❝✐❛ ❞♦s ❝✉❧t✐✈❛r❡s ♥♦s ✈ár✐♦s ❛♥♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✸✳✹ ▼é❞✐❛s ❞♦s í♥❞✐❝❡s ❛♠❜✐❡♥t❛✐s ♣♦r ❜❧♦❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✸✳✺ ❈♦rr❡❧❛çõ❡s ❧✐♥❡❛r❡s ❡ ❞❡ ❙♣❡❛r♠❛♥ ❡♥tr❡ ♣❛r❡s ❞❡ í♥❞✐❝❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✸✳✻ ❈♦❡✜❝✐❡♥t❡s ❛♥❣✉❧❛r❡s ❛❥✉st❛❞♦s ♥❛s ❖♣çõ❡s I ❡II ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹

✸✳✼ ❙♦♠❛ ❞♦s q✉❛❞r❛❞♦s ❞♦s ❘❡sí❞✉♦s ♣❛r❛ ❛ ♠é❞✐❛ ❞♦s í♥❞✐❝❡s ❛♠❜✐❡♥t❛✐s ♦❜t✐❞♦s ♥❛ ❖♣çã♦ II ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺

✸✳✽ ❘❡s✉❧t❛❞♦s ❞♦s t❡st❡s F ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻

✸✳✾ ❱❛❧♦r❡s ❡st✐♠❛❞♦s ♣❛r❛ α✱ β ❡α′ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽

✸✳✶✵ ❈❧❛ss✐✜❝❛çã♦ ❞♦s ❝✉❧t✐✈❛r❡s ♥❛ ❖♣çã♦I ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾

✸✳✶✶ ❘❡s✉❧t❛❞♦s ❞♦ ❛❥✉st❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✸✳✶✷ ❘❡s✉❧t❛❞♦s ❞♦ t❡st❡ t ✲ ❈✉❧t✐✈❛r❡s ❞♦♠✐♥❛♥t❡s ❡ ❞♦♠✐♥❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸

✸✳✶✸ ❘❡s✉❧t❛❞♦s ❞♦s ♠ét♦❞♦s ❞❡ ❝♦♠♣❛r❛çã♦ ♠ú❧t✐♣❧❛ ❞❡ ❇♦♥❢❡rr♦♥✐ ❡ ❞❡ ❙❝❤❡✛é ❛♦ ♥í✈❡❧ ❞❡ ✺%✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹

✸✳✶✹ ❈❧❛ss✐✜❝❛çã♦ ❞♦s ❝✉❧t✐✈❛r❡s ♥❛ ❖♣çã♦II ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺

✸✳✶✺ ❈♦♠♣♦s✐çã♦ ❞♦s ❝♦♥t♦r♥♦s s✉♣❡r✐♦r❡s ❛♥♦ ❛ ❛♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✸✳✶✻ ❋✉♥çõ❡s ♦❜❥❡❝t✐✈♦ ✉t✐❧✐③❛❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✸✳✶✼ ▼á①✐♠♦s ❞❛s ❢✉♥çõ❡s ♦❜❥❡❝t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✸✳✶✽ ❆❣r✉♣❛♠❡♥t♦ ❞♦s ❝✉❧t✐✈❛r❡s s❡❣✉♥❞♦ ❛ ♣r❡s❡♥ç❛ ♥♦s ❛♥♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✸✳✶✾ ❱❛❧♦r❡s ❡st✐♠❛❞♦s ♣❛r❛ ❛ ❢✉♥çã♦ f1 r❡❧❛t✐✈♦s ❛♦s ❝✉❧t✐✈❛r❡s ❞♦ ●r✉♣♦ q✉❛tr♦ ✼✶ ✸✳✷✵ ❘❡s✉❧t❛❞♦s ❞♦s ❚❡st❡s F ♣❛r❛ ❡❢❡✐t♦s ❡ ✐♥t❡r❛❝çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸

❳❱■ ▲✐st❛ ❞❡ ❚❛❜❡❧❛s

✸✳✷✶ ▼ét♦❞♦ ❞❡ ❙❝❤❡✛é ❡ ❇♦♥❢❡rr♦♥✐ ♣❛r❛ ♦s ❝✉❧t✐✈❛r❡s ❞♦ ●r✉♣♦ ✸ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✸✳✷✷ ▼ét♦❞♦ ❞❡ ❙❝❤❡✛é ❡ ❇♦♥❢❡rr♦♥✐ ♣❛r❛ ♦s ❝✉❧t✐✈❛r❡s ❞♦ ●r✉♣♦ ✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✸✳✷✸ ▼ét♦❞♦ ❞❡ ❙❝❤❡✛é ♣❛r❛ ♦s ❛♥♦s ❞♦ ●r✉♣♦ ✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✸✳✷✹ ▼ét♦❞♦ ❞❡ ❙❝❤❡✛é ♣❛r❛ ♦s ❛♥♦s ❞♦ ●r✉♣♦ ✽ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✸✳✷✺ ▼ét♦❞♦ ❞❡ ❙❝❤❡✛é ❡ ❇♦♥❢❡rr♦♥✐ ♣❛r❛ ♦s ❝✉❧t✐✈❛r❡s ❞♦ ●r✉♣♦ ✶✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✸✳✷✻ ▼ét♦❞♦ ❞❡ ❙❝❤❡✛é ❡ ❇♦♥❢❡rr♦♥✐ ♣❛r❛ ♦s ❝✉❧t✐✈❛r❡s ❞♦ ●r✉♣♦ ✶✻ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✸✳✷✼ ▼ét♦❞♦ ❞❡ ❙❝❤❡✛é ♣❛r❛ ♦s ❛♥♦s ❞♦ ●r✉♣♦ ✶✽ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✸✳✷✽ ▼ét♦❞♦ ❞❡ ❙❝❤❡✛é ♣❛r❛ ♦s ❛♥♦s ❞♦ ●r✉♣♦ ✶✾ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻

✹✳✶ ❈♦❡✜❝✐❡♥t❡s ❛❥✉st❛❞♦s ❡ t❡st❡st ♥❛ ❖♣çã♦ I ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺

✹✳✷ ❈♦❡✜❝✐❡♥t❡s ❛❥✉st❛❞♦s ❡ t❡st❡st ♥❛ ❖♣çã♦ II ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻

▲✐st❛ ❞❡ ❋✐❣✉r❛s

✷✳✶ P♦♥t♦ ❞❡ ■♥t❡rs❡❝çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✷✳✷ ❘❡❝t❛s P❛r❛❧❡❧❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✷✳✸ ❚r❛ç❛❞♦ ❞♦ ❝♦♥t♦r♥♦ s✉♣❡r✐♦r q✉❛♥❞♦ _θ¯_{1 ≤θmin ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷}

✷✳✹ ❚r❛ç❛❞♦ ❞♦ ❝♦♥t♦r♥♦ s✉♣❡r✐♦r q✉❛♥❞♦ θmin <θ¯1 < θmax ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸

✷✳✺ ❚r❛ç❛❞♦ ❞♦ ❝♦♥t♦r♥♦ s✉♣❡r✐♦r q✉❛♥❞♦ _θ¯_{1 ≥θmax ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸}

✷✳✻ ❈♦♥t♦r♥♦ s✉♣❡r✐♦r ❝♦♠ ❞♦✐s ❝✉❧t✐✈❛r❡s ❞♦♠✐♥❛♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✷✳✼ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ❝✉❧t✐✈❛r❡s ❞♦♠✐♥❛♥t❡s ❡ ♥ã♦ ❞♦♠✐♥❛♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺

✸✳✶ ❈♦♥t♦r♥♦ ❙✉♣❡r✐♦r ♥❛ ❖♣çã♦ I ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶

❆✳✶ ❈♦♥t♦r♥♦ ❙✉♣❡r✐♦r ♥♦ ❛♥♦ ❞❡ ✶✾✽✻ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻ ❆✳✷ ❈♦♥t♦r♥♦ ❙✉♣❡r✐♦r ♥♦ ❛♥♦ ❞❡ ✶✾✽✼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼ ❆✳✸ ❈♦♥t♦r♥♦ ❙✉♣❡r✐♦r ♥♦ ❛♥♦ ❞❡ ✶✾✽✽ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽ ❆✳✹ ❈♦♥t♦r♥♦ ❙✉♣❡r✐♦r ♥♦ ❛♥♦ ❞❡ ✶✾✽✾ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✾ ❆✳✺ ❈♦♥t♦r♥♦ ❙✉♣❡r✐♦r ♥♦ ❛♥♦ ❞❡ ✶✾✾✵ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✵ ❆✳✻ ❈♦♥t♦r♥♦ ❙✉♣❡r✐♦r ♥♦ ❛♥♦ ❞❡ ✶✾✾✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶ ❆✳✼ ❈♦♥t♦r♥♦ ❙✉♣❡r✐♦r ♥♦ ❛♥♦ ❞❡ ✶✾✾✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷ ❆✳✽ ❈♦♥t♦r♥♦ ❙✉♣❡r✐♦r ♥♦ ❛♥♦ ❞❡ ✶✾✾✺ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸ ❆✳✾ ❈♦♥t♦r♥♦ ❙✉♣❡r✐♦r ♥♦ ❛♥♦ ❞❡ ✶✾✾✼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹ ❆✳✶✵ ❈♦♥t♦r♥♦ ❙✉♣❡r✐♦r ♥♦ ❛♥♦ ❞❡ ✶✾✾✾ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✺

❈❛♣ít✉❧♦ ✶

■♥tr♦❞✉çã♦

❯♠ ❞♦s ❛s♣❡❝t♦s ✐♠♣♦rt❛♥t❡s ❞♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞✉♠❛ té❝♥✐❝❛✱ ❝♦rr❡s♣♦♥❞❡ ❛♦ ❛❧❛r❣❛♠❡♥t♦ ❞♦ s❡✉ ❞♦♠í♥✐♦ ❞❡ ❛♣❧✐❝❛çã♦✳

◆❛ s✉❛ ❢♦r♠✉❧❛çã♦ ✉s✉❛❧ ❛ ❆♥á❧✐s❡ ❈♦♥❥✉♥t❛ ❞❡ ❘❡❣r❡ssõ❡s✱ ❆❈❘✱ ❡♥q✉❛❞r❛✲s❡ ♥♦ ❝♦♥✲ ❥✉♥t♦ ❞❛s té❝♥✐❝❛s ✉t✐❧✐③❛❞❛s✱ ✈❡r ❆❛st✈❡✐t ❡ ▼❡❥③❛ ✭✶✾✾✷✮✱ ♣❛r❛ ♦ ❡st✉❞♦ ❞❛s ✐♥t❡r❛❝çõ❡s ✭❣❡♥♦t✐♣♦s ① ❛♠❜✐❡♥t❡✮✳ ▼❛✐s ❝♦♥❝r❡t❛♠❡♥t❡✱ ♣❡rt❡♥❝❡ ❛♦ ❣r✉♣♦ ❞❛s té❝♥✐❝❛s ❜❛s❡❛❞❛s ♥♦ ❛❥✉st❛♠❡♥t♦ ❞❡ r❡❣r❡ssõ❡s✳ ❊st❛s r❡❣r❡ssõ❡s sã♦ ❧✐♥❡❛r❡s✱ ✉♠❛ ♣♦r ❝✉❧t✐✈❛r✱ t❡♥❞♦ ❝♦♠♦ ✈❛r✲ ✐á✈❡❧ ❞❡♣❡♥❞❡♥t❡ ♦ r❡♥❞✐♠❡♥t♦✳ ❆ ✈❛r✐á✈❡❧ ❝♦♥tr♦❧❛❞❛✱ ♦ ❝❤❛♠❛❞♦ í♥❞✐❝❡ ❛♠❜✐❡♥t❛❧✱ ♠❡❞❡✱ ♣❛r❛ ❝❛❞❛ ♣❛r ✭❧♦❝❛❧✱ ❛♥♦✮✱ ❛ r❡s♣❡❝t✐✈❛ ❝❛♣❛❝✐❞❛❞❡ ♣r♦❞✉t✐✈❛✳

❉❡s❞❡ ❛ ♦r✐❣❡♠ ❞❛ s✉❛ ❛♣❧✐❝❛çã♦ ❡ ❞✉r❛♥t❡ ❛❧❣✉♥s ❛♥♦s ❛ ❆❈❘ ❡r❛ ❛♣❧✐❝❛❞❛ ❛ r❡❞❡s ❞❡ ❡♥s❛✐♦s ❡♠ ❜❧♦❝♦s ❝❛s✉❛❧✐③❛❞♦s✳ ❙❡❣✉✐♥❞♦✲s❡ ●✉s♠ã♦ ✭✶✾✽✺✮ ❡ ✭✶✾✽✻ ❛✮ ♦s í♥❞✐❝❡s ❛♠❜✐❡♥t❛✐s ❝♦rr❡s♣♦♥❞❡♥t❡s ❛♦s ❞✐❢❡r❡♥t❡s ❜❧♦❝♦s ❡r❛♠ ♠❡❞✐❞♦s ♣❡❧♦s r❡s♣❡❝t✐✈♦s r❡♥❞✐♠❡♥t♦s ♠é❞✐♦s✳ P♦st❡r✐♦r♠❡♥t❡✱ ♦s ❡♥s❛✐♦s ♣❛ss❛r❛♠ ❛ s❡r s♦❜r❡t✉❞♦ ❞♦ t✐♣♦ α ✲ ❞❡s✐❣♥s✱ ❧♦❣♦ ❝♦♠ ❜❧♦❝♦s

✐♥❝♦♠♣❧❡t♦s✱ ✈❡r P❛tt❡rs♦♥ ❛♥❞ ❲✐❧❧✐❛♠s ✭✶✾✼✻✮✳ ❉❡✐①♦✉ ♣♦✐s✱ ❞❡ s❡ ♣♦❞❡r ♠❡❞✐r ♦s í♥❞✐❝❡s ❛♠❜✐❡♥t❛✐s ❞♦s ❜❧♦❝♦s ❛tr❛✈és ❞♦s r❡s♣❡❝t✐✈♦s r❡♥❞✐♠❡♥t♦s ♠é❞✐♦s✳ P❛r❛ ✉❧tr❛♣❛ss❛r ❡st❛ ❞✐✜❝✉❧❞❛❞❡✱ ❢♦r❛♠ ✐♥tr♦❞✉③✐❞♦s ♦s í♥❞✐❝❡s ❛♠❜✐❡♥t❛✐s L2✱ ✈❡r ▼❡①✐❛ ❡t ❛❧ ✭✶✾✾✾✮✳ ❊st❡s

í♥❞✐❝❡s sã♦ ❛❥✉st❛❞♦s ❥✉♥t❛♠❡♥t❡ ❝♦♠ ♦s ❝♦❡✜❝✐❡♥t❡s ❞❛s r❡❣r❡ssõ❡s✱ ❛tr❛✈és ❞❛ ♠✐♥✐♠✐③❛çã♦ ❞✉♠❛ ❢✉♥çã♦ ♦❜❥❡❝t✐✈♦ q✉❛❞rát✐❝❛✳ P❡r❡✐r❛ ✭✷✵✵✹✮ ❞❡s❡♥✈♦❧✈❡ ❞✉♠❛ ❢♦r♠❛ s✐st❡♠át✐❝❛ ❛ ❆❈❘✱ ✉t✐❧✐③❛♥❞♦ í♥❞✐❝❡s ❛♠❜✐❡♥t❛✐s L2✳ ◆♦ ❡♥t❛♥t♦✱ s✉❜❥❛❝❡♥t❡ ❛♦ s❡✉ tr❛t❛♠❡♥t♦✱ ❡stã♦

♦s ♣r❡ss✉♣♦st♦s ❞❡ q✉❡ ♦s ❡♥s❛✐♦s ❢♦r❛♠ r❡❛❧✐③❛❞♦s ♥✉♠ ♥ú♠❡r♦ r❡❞✉③✐❞♦ ❞❡ ❛♥♦s ❡ q✉❡ s❡ tr❛❜❛❧❤♦✉ ❝♦♠ ✉♠ ❝♦♥❥✉♥t♦ ❞❛❞♦ ❞❡ ❝✉❧t✐✈❛r❡s✳

◗✉❛♥❞♦ ♣❛ss❛♠♦s ❛ ❝♦♥s✐❞❡r❛r ♣❧❛♥♦s ❞❡ ♠❡❧❤♦r❛♠❡♥t♦✱ t❡♠♦s ❡♥s❛✐♦s r❡❛❧✐③❛❞♦s ❛♦ ❧♦♥❣♦ ❞✉♠ ♥ú♠❡r♦ ❝♦♥s✐❞❡rá✈❡❧ ❞❡ ❛♥♦s ❡ ✉♠ ❝♦♥❥✉♥t♦ ❛❜❡rt♦ ❞❡ ❝✉❧t✐✈❛r❡s✳ ❈♦♠ ❡❢❡✐t♦✱ ❛♦ ❧♦♥❣♦ ❞❛ r❡❛❧✐③❛çã♦ ❞♦ ♣❧❛♥♦ ❞❡ ♠❡❧❤♦r❛♠❡♥t♦✱ ❤❛✈❡rá ❡♥tr❛❞❛ ❡ s❛í❞❛ ❞❡ ❝✉❧t✐✈❛r❡s✳

❖ ♥♦ss♦ ♦❜❥❡❝t✐✈♦ é ♠♦str❛r ❝♦♠♦ ❛♣❧✐❝❛r ❛ ❆❈❘ ♥❛ ❝♦♥❞✉çã♦ ❞❡ ♣❧❛♥♦s ❞❡ ♠❡❧❤♦r❛♠❡♥t♦✳ ❉❛❞❛ ❛ s✐♥❣✉❧❛r✐❞❛❞❡ ❞❡st❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦✱ r❡s♦❧✈❡♠♦s ❛♣♦✐❛r✲♠♦✲♥♦s ♥♦ ❡st✉❞♦ ❞✉♠ ♣❧❛♥♦

✷ ■♥tr♦❞✉çã♦

❞❡ ♠❡❧❤♦r❛♠❡♥t♦ ❞❛❞♦✿ ♦ ❞♦ ❚r✐❣♦ ▼♦❧❡ ❡♠ P♦rt✉❣❛❧ ✭✶✾✽✻ ✲ ✷✵✵✵✮✳ ❖ ♥♦ss♦ tr❛❜❛❧❤♦✱ ♣❛r❛ ❛❧é♠ ❞♦ ♣r✐♠❡✐r♦ ❝❛♣ít✉❧♦ ❝♦rr❡s♣♦♥❞❡♥t❡ à ■♥tr♦❞✉çã♦ ❡ ❞♦ q✉✐♥t♦ ❝❛♣ít✉❧♦ ❝♦rr❡s♣♦♥❞❡♥t❡ às ❈♦♥❝❧✉sõ❡s ❋✐♥❛✐s ❡ ❚r❛❜❛❧❤♦s ❋✉t✉r♦s✱ ❛rt✐❝✉❧❛✲s❡ ♥♦s três ❝❛♣ít✉❧♦s✿

✷✳ ❆♥á❧✐s❡ ❈♦♥❥✉♥t❛ ❞❡ ❘❡❣r❡ssõ❡s❀

✸✳ P❧❛♥♦ ❞❡ ▼❡❧❤♦r❛♠❡♥t♦ ❞♦ ❚r✐❣♦ ▼♦❧❡❀ ✹✳ ❮♥❞✐❝❡s ❆♠❜✐❡♥t❛✐s✳

◆♦ ♣r✐♠❡✐r♦ ❞❡st❡s ❝❛♣ít✉❧♦s✱ ❞❡s❡♥✈♦❧✈❡♠♦s ♦s ❛s♣❡❝t♦s ❞❛ ❆❈❘ ❞❡ q✉❡ ♥❡❝❡ss✐t❛♠♦s ♣❛r❛ ❛ ❞✐s❝✉ssã♦ ❞❡ ♣❧❛♥♦s ❞❡ ♠❡❧❤♦r❛♠❡♥t♦✳ ❈♦♠❡ç❛♠♦s ♣♦r ❡st✉❞❛r ❛s q✉❡stõ❡s r❡❧❛t✐✈❛s ❛♦ ❛❥✉st❛♠❡♥t♦✳ ❖❜s❡r✈❡✲s❡ q✉❡✱ q✉❛♥❞♦ s❡ ✉t✐❧✐③❛♠ í♥❞✐❝❡s ❛♠❜✐❡♥t❛✐s L2✱ s❡ ❡st✐♠❛♠

♥ã♦ só ♦s ❝♦❡✜❝✐❡♥t❡s ❞❛s r❡❣r❡ssõ❡s ❝♦♠♦ t❛♠❜é♠ ♦s í♥❞✐❝❡s ❛♠❜✐❡♥t❛✐s✳ ❈❧❛ss✐❝❛♠❡♥t❡✱ q✉❛♥❞♦ s❡ ❛❥✉st❛✈❛ ✉♠❛ r❡❣r❡ssã♦ ❧✐♥❡❛r✱ ❛ ♠❛tr✐③ ❞♦ ♠♦❞❡❧♦ ❡r❛ s✉♣♦st❛ ❝♦♥❤❡❝✐❞❛✳ ◆❡st❡ ❡♥q✉❛❞r❛♠❡♥t♦ ❣❡♥❡r❛❧✐③❛❞♦ ❛ q✉❡ ❝❤❛♠❛♠♦s ♠í♥✐♠♦s q✉❛❞r❛❞♦s ❡str✉t✉r❛❞♦s ❛ ♠❛tr✐③ ❞♦ ♠♦❞❡❧♦ é ❛♣❡♥❛s ❝♦♥❤❡❝✐❞❛ ❛ ♠❡♥♦s ❞✉♠ ✈❡❝t♦r ❞❡ ❡str✉t✉r❛ q✉❡✱ ♥♦ ❝❛s♦ ❞❛ ❆❈❘✱ é ♦ ✈❡❝t♦r ❞♦s í♥❞✐❝❡s ❛♠❜✐❡♥t❛✐s✳ ❈♦♥s✐❞❡r❛♠♦s ❡♠ ♣❛rt✐❝✉❧❛r ♦ ❝❛s♦ ❞❡ r❡❞❡s ❞❡ ❡♥s❛✐♦s q✉❡ s❡ ❢r❛❝❝✐♦♥❛♠ ❡♠ s✉❜✲r❡❞❡s✱ ❝♦♥st✐t✉í❞❛s ♣♦r ❡♥s❛✐♦s ❝♦♠ ❜❧♦❝♦s✱ ❝♦♥t❡♥❞♦ t♦❞♦s ♦s ❝✉❧t✐✈❛r❡s ♣r❡s❡♥t❡s ♥❛ s✉❜✲r❡❞❡✳ ❍❛✈❡♥❞♦ ✉♠❛ ♦r❞❡♠ ❡♥tr❡ s✉❜✲r❡❞❡s ❡ ❝✉❧t✐✈❛r❡s ❝♦♠✉♥s ❛ r❡❞❡s ❛❞❥❛❝❡♥t❡s✱ ❛ ❛♥á❧✐s❡ ❞❡st❡s ❝❛s♦s ❛♣r❡s❡♥t❛✱ ❝♦♠♦ ✈❡r❡♠♦s✱ ♣r♦♣r✐❡❞❛❞❡s ✐♥t❡r❡ss❛♥t❡s✳ P❛rt✐❝✉❧❛r♠❡♥t❡✱ tr❛t❛r❡♠♦s ♦ ❝❛s♦ ❡♠ q✉❡ ❝❛❞❛ s✉❜✲r❡❞❡ ❝♦rr❡s♣♦♥❞❡ ❛ ✉♠ ❛♥♦✱ ❞❛♥❞♦ ❛ss✐♠ ❧✉❣❛r ❛ ❞♦✐s t✐♣♦s ❞❡ ❛❥✉st❛♠❡♥t♦s✳ ❖ ❛❥✉st❛♠❡♥t♦ ❣❧♦❜❛❧ ❡♠ q✉❡ s❡ ✉t✐❧✐③❛♠ ♦s ❞❛❞♦s ❞❡ t♦❞♦s ♦s ❛♥♦s ❞✐s♣♦♥í✈❡✐s✱ ♦ q✉❛❧ ❞❡s✐❣♥❛♠♦s ♣♦r ❖♣çã♦I ❡ ♦ ❝♦♥❥✉♥t♦ ❞♦s ❛❥✉st❛♠❡♥t♦s

❝♦rr❡s♣♦♥❞❡♥t❡s ❛ ❝❛❞❛ ❛♥♦ q✉❡ ❞❡s✐❣♥❛♠♦s ♣♦r ❖♣çã♦ II✳ ❙❡❣✉❡✲s❡ ♦ ❡st✉❞♦ ❞❡ q✉❡stõ❡s

❞❡ ✐♥❢❡rê♥❝✐❛ ❡st❛tíst✐❝❛✳ Pr♦❝✉r❛✲s❡ ❢✉♥❞❛♠❡♥t❛❧♠❡♥t❡ ❞❡s❡♥✈♦❧✈❡r té❝♥✐❝❛s✱ ♣❛r❛ ❛✈❛❧✐❛r ❛ ❡st❛❜✐❧✐❞❛❞❡ ❞♦s ❝♦♠♣♦rt❛♠❡♥t♦s ❞♦s ❝✉❧t✐✈❛r❡s ❡ ♣❛r❛ ❝♦♠♣❛r❛r ❝✉❧t✐✈❛r❡s✳ ❯t✐❧✐③❛♠♦s ❢✉♥çõ❡s ❧✐♥❡❛r❡s ❞♦ t✐♣♦ Uj,l = αj,l +βj,lx✱ ♦♥❞❡ ♦s í♥❞✐❝❡s ✐♥❢❡r✐♦r❡s j ❡ l r❡♣r❡s❡♥t❛♠ ♦

❝✉❧t✐✈❛r ❡ ♦ ❛♥♦ ❡♠ ❛♥á❧✐s❡ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❖ ✈❛❧♦r ❞❡ x♣❡rt❡♥❝❡ ❛♦ ✐♥t❡r✈❛❧♦ ❞❡ ✈❛r✐❛çã♦

❞♦s í♥❞✐❝❡s ❛♠❜✐❡♥t❛✐s ❛❥✉st❛❞♦s✳ ❊st❡ ✈❛❧♦r ❞❡✈❡ s❡r ❡s❝♦❧❤✐❞♦ ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦s ♦❜❥❡❝t✐✈♦s ❞♦s ♠❡❧❤♦r❛❞♦r❡s✳ ❈♦♠ ❡❢❡✐t♦✱ ❛♦ ✉t✐❧✐③❛r✲s❡ ✉♠❛ ❞❡st❛s ❢✉♥çõ❡s ❡stã♦✲s❡ ❛ ❝♦♠♣❛r❛r ♦s ✈❛❧♦r❡s ❛❥✉st❛❞♦s ♣❛r❛ ♦s ❝✉❧t✐✈❛r❡s ❡ ♣❛r❛ ❡ss❡ ✈❛❧♦r ❞♦ í♥❞✐❝❡ ❛♠❜✐❡♥t❛❧✳

■♥tr♦❞✉çã♦ ✸

◆♦ t❡r❝❡✐r♦ ❝❛♣ít✉❧♦✱ t❡♥t❛♠♦s ♠♦str❛r ✉♠❛ ❛♣❧✐❝❛çã♦ ❞❛ ❆❈❘ ❛ ♣❧❛♥♦s ❞❡ ♠❡❧❤♦r❛♠❡♥t♦✱ ❡♠ ♣❛rt✐❝✉❧❛r ♦ ❞♦ ❚r✐❣♦ ▼♦❧❡ ❡♠ P♦rt✉❣❛❧ ✭✶✾✽✻ ✲ ✷✵✵✵✮✳ ❖ ♣r✐♠❡✐r♦ ♣r♦❜❧❡♠❛ q✉❡ s❡ ♣õ❡ é ♦ ❞❛ ✈❡r✐✜❝❛çã♦ ❞❛ ❡st❛❜✐❧✐❞❛❞❡ ❞♦s r❡s✉❧t❛❞♦s✳ ❊st❡ ♣r♦❜❧❡♠❛ é ❛♥❛❧✐s❛❞♦ ♣♦r ❞✉❛s ❡t❛♣❛s✳ ◆❛ ♣r✐♠❡✐r❛✱ ♣r♦❝✉r❛✲s❡ r❡❧❛❝✐♦♥❛r ♦s í♥❞✐❝❡s ❛♠❜✐❡♥t❛✐s ❛❥✉st❛❞♦s ❣❧♦❜❛❧♠❡♥t❡ ❝♦♠ ♦s ❛❥✉st❛❞♦s ❛♥♦ ❛ ❛♥♦✳ ❱❡r✐✜❝❛✲s❡✱ ♣❛r❛ ♦ ❝❛s♦ ❛♥❛❧✐s❛❞♦✱ ✉♠ ❛❧t♦ ❣r❛✉ ❞❡ ❝♦♠♣❛t✐❜✐❧✐❞❛❞❡ ❡♥tr❡ ♦s ❞♦✐s ❝♦♥❥✉♥t♦s ❞❡ í♥❞✐❝❡s ❛♠❜✐❡♥t❛✐s✳ ◆❛ s❡❣✉♥❞❛ ❡t❛♣❛✱ ❡st✉❞❛✲s❡ ❛ ❡st❛❜✐❧✐❞❛❞❡ ❞♦s ❝✉❧t✐✈❛r❡s ✉t✐❧✐③❛❞♦s ❡♠ ✈ár✐♦s ❛♥♦s✳ ❉❡s✐❣♥❛♠✲s❡ ♣♦rβ ✲ ❡stá✈❡❧ ♦s ❝✉❧t✐✈❛r❡s ♣❛r❛ ♦s

q✉❛✐s ♥ã♦ s❡ r❡❥❡✐t❛ ❛ ❤✐♣ót❡s❡ ❞❡ ✐❣✉❛❧❞❛❞❡ ❞♦s ❝♦❡✜❝✐❡♥t❡s ❛♥❣✉❧❛r❡s ❞❛s r❡❝t❛s ❞❡ r❡❣r❡ssã♦ ❛❥✉st❛❞❛s✱ ❡♠ ✈ár✐♦s ❛♥♦s✱ ♣❛r❛ ❝❛❞❛ ✉♠ ❞❡ss❡s ❝✉❧t✐✈❛r❡s✳ ◆❛ ❛♣❧✐❝❛çã♦ ♣rát✐❝❛ q✉❡ ✈❛♠♦s ❛♣r❡s❡♥t❛r✱ ❛♣❡♥❛s três ❝✉❧t✐✈❛r❡s ❡♠ ✷✷ ♥ã♦ s❡ r❡✈❡❧❛♠ β✲ ❡stá✈❡✐s✳

❱❡r✐✜❝❛❞❛ ❛ ❡①✐stê♥❝✐❛ ❞❡ ❡st❛❜✐❧✐❞❛❞❡ ❞♦s r❡s✉❧t❛❞♦s✱ ♣♦❞❡♠♦s ❛❝❡✐t❛r ❛ ✉t✐❧✐③❛çã♦ ❞❛ ❆❈❘ ❡ ♣r♦ss❡❣✉✐r ❛ ♥♦ss❛ ❛♥á❧✐s❡✳ P❛ss❛♠♦s ❡♥tã♦ à ❝❧❛ss✐✜❝❛çã♦ ❡ s❡❧❡❝çã♦ ❞♦s ❝✉❧t✐✈❛r❡s✱ ♦ q✉❡ é ❢❡✐t♦ ♣❛r❛ ❝❛❞❛ ✉♠❛ ❞❛s ❞✉❛s ♦♣çõ❡s✳ ◆♦ q✉❡ r❡s♣❡✐t❛ à ❝❧❛ss✐✜❝❛çã♦✱ ♦s ❝✉❧t✐✈❛r❡s ❝✉❥❛ r❡❝t❛ ❞❡ r❡❣r❡ssã♦ ❛❥✉st❛❞❛ t❡♠ ❝♦❡✜❝✐❡♥t❡ ❛♥❣✉❧❛rβ s✉♣❡r✐♦r❬✐♥❢❡r✐♦r❪ ❛ ✉♠ sã♦ ✐♥t❡♥✲

s✐✈♦s❬❡①t❡♥s✐✈♦s❪✱ ✐♥t❡r❡ss❛♥❞♦ ✈❡r✐✜❝❛r s❡β ❞✐❢❡r❡ s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ❞❡ ✉♠✳ ❘❡❧❛t✐✈❛♠❡♥t❡

à s❡❧❡❝çã♦✱ ✉t✐❧✐③❛✲s❡ ♦ ♠ét♦❞♦ ❞♦ ❝♦♥t♦r♥♦ s✉♣❡r✐♦r ❞❡✜♥✐❞♦ ♣❡❧❛s r❡❣r❡ssõ❡s ❛❥✉st❛❞❛s✳ ❊st❡ ❝♦♥t♦r♥♦ s✉♣❡r✐♦r é ✉♠❛ ♣♦❧✐❣♦♥❛❧ ❝♦♥✈❡①❛✳ ❖s ❝✉❧t✐✈❛r❡s ❝✉❥❛s r❡❝t❛s ❞❡ r❡❣r❡ssã♦ ❛❥✉st❛❞❛s ✐♥t❡❣r❛♠ ♦ ❝♦♥t♦r♥♦ s✉♣❡r✐♦r✱ sã♦ ❝✉❧t✐✈❛r❡s ❞♦♠✐♥❛♥t❡s✳ ❆ ❝❛❞❛ ✉♠ ❞❡st❡s ❝♦r✲ r❡s♣♦♥❞❡ ✉♠ ✐♥t❡r✈❛❧♦ ❞❡ ❞♦♠✐♥â♥❝✐❛✳ ❖s r❡st❛♥t❡s ❝✉❧t✐✈❛r❡s✱ ❞❡✈❡♠ s❡r ❝♦♠♣❛r❛❞♦s ❝♦♠ ♦s ❝✉❧t✐✈❛r❡s ❞♦♠✐♥❛♥t❡s✱ ♣❛r❛ ✈❡r s❡ sã♦ s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ❞♦♠✐♥❛❞♦s✳ ❉❛❞♦ ♣r❡t❡♥❞❡r✲s❡ ❝✉❧t✐✈❛r❡s q✉❡ ❛♣r♦✈❡✐t❛♠ ❛❞❡q✉❛❞❛♠❡♥t❡ ❜♦❛s ❝♦♥❞✐çõ❡s ❞❡ ❢❡rt✐❧✐❞❛❞❡✱ sã♦ s♦❜r❡t✉❞♦ ✐♠✲ ♣♦rt❛♥t❡s ♦s ❝✉❧t✐✈❛r❡s ❞♦♠✐♥❛♥t❡s ❝♦rr❡s♣♦♥❞❡♥t❡s ❛♦s ✐♥t❡r✈❛❧♦s ❞❡ ❞♦♠✐♥â♥❝✐❛ à ❞✐r❡✐t❛✳ ❉❡✈❡ s❛❧✐❡♥t❛r✲s❡ q✉❡✱ ♥♦ ❝❛s♦ ❞♦ ♠❡❧❤♦r❛♠❡♥t♦ ❞♦ tr✐❣♦ ♠♦❧❡✱ ♣❛r❛ ❛ ♦♣çã♦I✱ ♦s ❝✉❧t✐✈❛r❡s

❞♦♠✐♥❛♥t❡s à ❞✐r❡✐t❛ ♣❡r♠❛♥❡❝❡r❛♠ ♥♦ ♣r♦❣r❛♠❛ ❛té ❛♦ ✜♥❛❧✳

◆♦ ❡st✉❞♦ ❞♦s ❝♦♥t♦r♥♦s s✉♣❡r✐♦r❡s ❡ ❞❛ ❝❧❛ss✐✜❝❛çã♦ ❞♦s ❝✉❧t✐✈❛r❡s ❛♥♦ ❛ ❛♥♦ ✈❡r✐✜❝❛♠♦s ❛ ♣r❡s❡♥ç❛ ❞❡ ❛❧❣✉♠❛s s✐t✉❛çõ❡s ❞✐❢í❝❡✐s ❞❡ ❡①♣❧✐❝❛r✿ ❝✉❧t✐✈❛r❡s q✉❡ ♥✉♠ ❛♥♦ ❡r❛♠ ❞♦♠✐♥❛♥t❡s à ❞✐r❡✐t❛✱ β✲❡stá✈❡❧ ❡ ❝❧❛ss✐✜❝❛❞♦s ❝♦♠♦ ✐♥t❡♥s✐✈♦s✱ ♣♦r ✈❡③❡s ♥ã♦ ❢♦r❛♠ ✉t✐❧✐③❛❞♦s ♥♦ ❛♥♦

s❡❣✉✐♥t❡✳ ❊st❡ é ✉♠ ♣♦♥t♦ ♠✉✐t♦ ✐♥t❡r❡ss❛♥t❡✱ ♣♦✐s ❛♣♦♥t❛ ♣❛r❛ ❛ ✉t✐❧✐❞❛❞❡ ❞❛ ❆❈❘ ❝♦♠♦ ✐♥str✉♠❡♥t♦ ♥❛ t♦♠❛❞❛ ❞❡ ❞❡❝✐sã♦✱ r❡❧❛t✐✈❛♠❡♥t❡ à ♣❡r♠❛♥ê♥❝✐❛ ❞❡ ❝✉❧t✐✈❛r❡s ♥♦ ♣❧❛♥♦ ❞❡ ♠❡❧❤♦r❛♠❡♥t♦✳

❈♦♠ ♦ ♦❜❥❡❝t✐✈♦ ❞❡ ❛✈❛❧✐❛r ♦ ♣r♦❣r❡ss♦ ❞♦ ♣❧❛♥♦ ❞❡ ♠❡❧❤♦r❛♠❡♥t♦✱ ❡st✉❞❛♠♦s ❡♠ s❡❣✉✐❞❛✱ ❛ ❡✈♦❧✉çã♦ ❞♦s ✈❛❧♦r❡s ♠á①✐♠♦s t♦♠❛❞♦s ♣❡❧❛s ❢✉♥çõ❡s ♦❜❥❡❝t✐✈♦ Uj,l✳ ◆♦ ❡♥t❛♥t♦✱ ❡ss❛

❡✈♦❧✉çã♦ r❡✈❡❧♦✉✲s❡ ❞✐❢í❝✐❧ ❞❡ ✐♥t❡r♣r❡t❛r ❞✐r❡❝t❛♠❡♥t❡✱ s❡♥❞♦ ♣♦r ✐ss♦ s✉❥❡✐t❛ ❛ ✉♠❛ ❛♥á❧✐s❡ ♣♦st❡r✐♦r✳

✹ ■♥tr♦❞✉çã♦

❝♦♥st✐t✉❡♠ ❡ss❡s ❣r✉♣♦s t✐✈❡ss❡♠ t✐❞♦ ✉♠ ❝♦♠♣♦rt❛♠❡♥t♦ ❤♦♠♦❣é♥❡♦✳ ❋♦✐ ♥♦ ❡♥t❛♥t♦ ♣♦s✲ sí✈❡❧✱ ❞❡t❡❝t❛r ❢r❡q✉❡♥t❡s ✈✐♦❧❛çõ❡s ❞❡st❛ r❡❣r❛✱ t❡♥❞♦ s✐❞♦ ♥❛❧❣✉♥s ❛♥♦s ♠❛♥t✐❞♦s ❝✉❧t✐✈❛r❡s ❛ ❡❧✐♠✐♥❛r ❡ ❡❧✐♠✐♥❛❞♦s✱ ♥♦✉tr♦s ❛♥♦s✱ ❝✉❧t✐✈❛r❡s ❞♦♠✐♥❛♥t❡s✳ ❱❡r✐✜❝♦✉✲s❡ ❛ss✐♠ ♠❛✐s ✉♠❛ ✈❡③✱ ♦ ✐♥t❡r❡ss❡ ❞❛ ❆❈❘ ❝♦♠♦ té❝♥✐❝❛ ❞❡ ❛❝♦♠♣❛♥❤❛♠❡♥t♦ ❞♦s ♣❧❛♥♦s ❞❡ ♠❡❧❤♦r❛♠❡♥t♦✳ ❘❡s✉♠✐♥❞♦✱ ♥❡st❡ ❝❛♣ít✉❧♦ ♣r♦❝✉rá♠♦s✱ r❡✈❡♥❞♦✲♥♦s ♥♦ P❧❛♥♦ ❞❡ ▼❡❧❤♦r❛♠❡♥t♦ ❞♦ ❚r✐❣♦ ▼♦❧❡✱ ♠♦str❛r ❝♦♠♦ é ♣♦ssí✈❡❧✿

• ✈❛❧✐❞❛r ❛ ✉t✐❧✐③❛çã♦ ❞❛ ❆❈❘ ♥❛ ❛♥á❧✐s❡ ❞♦s r❡s✉❧t❛❞♦s ❞❡ ♣❧❛♥♦s ❞❡ ♠❡❧❤♦r❛♠❡♥t♦❀

• ✉t✐❧✐③❛r✱ ❛tr❛✈és ❞❛ ❛♥á❧✐s❡ ❞♦s r❡s✉❧t❛❞♦s ❞❡ ❝❛❞❛ ❛♥♦✱ ❛ ❆❈❘ ❝♦♠♦ té❝♥✐❝❛ ❞❡ ❛❝♦♠♣❛♥❤❛♠❡♥t♦ ❞❡ ♣❧❛♥♦s ❞❡ ♠❡❧❤♦r❛♠❡♥t♦✳

❖ q✉❛rt♦ ❝❛♣ít✉❧♦ s✉r❣❡ ❝♦♠ ❛ t❡♥t❛t✐✈❛ ❞❡ s❡ ♣♦❞❡r ✐♥t❡r♣r❡t❛r ♠❡❧❤♦r ♦s ✈❛❧♦r❡s ♠á①✐✲ ♠♦s t♦♠❛❞♦s ♣❡❧❛s ❢✉♥çõ❡s ♦❜❥❡❝t✐✈♦✳ ❈♦♠ ❡❢❡✐t♦✱ ❡st❡s ❛♣r❡s❡♥t❛♠ ♦s❝✐❧❛çõ❡s ✐rr❡❣✉❧❛r❡s ❞❡ ❛♥♦ ♣❛r❛ ❛♥♦✱ ♠✉✐t♦ ♣♦ss✐✈❡❧♠❡♥t❡ ❛tr✐❜✉í✈❡✐s ❛ ❢❛❝t♦r❡s ❞❡ ❝❛rá❝t❡r ❝❧✐♠át✐❝♦✳ P❛r❛ t❡st❛r ❡st❛ ❝♦♥❥❡❝t✉r❛✱ ❛❥✉st❛✲s❡ ✉♠ ♠♦❞❡❧♦ ❧✐♥❡❛r ♣❛r❛ ♦s í♥❞✐❝❡s ❛♠❜✐❡♥t❛✐s✳ ◆❡st❡ ♠♦❞❡❧♦ ❝♦♥s✐❞❡r❛♠✲s❡ ✈❛r✐á✈❡✐s ❞✉♠♠② ❝♦rr❡s♣♦♥❞❡♥t❡s ❛✿

• ❛♥♦s❀

• ❧♦❝❛✐s❀

• ❣r✉♣♦s ❞❡ ❝✉❧t✐✈❛r❡s✳

❖s ❣r✉♣♦s ❞❡ ❝✉❧t✐✈❛r❡s sã♦ ♦s ♠❡s♠♦s q✉❡ ❛trás t✐♥❤❛♠ s✐❞♦ ❝♦♥s✐❞❡r❛❞♦s✳ ❖s ❝♦❡✜❝✐❡♥t❡s ❞❛s ✈❛r✐á✈❡✐s ❞✉♠♠② ❛ss♦❝✐❛❞♦s ❛ ❛♥♦s sã♦ ✉t✐❧✐③❛❞♦s ♣❛r❛ ❡①♣r✐♠✐r ❛s ❝❛♣❛❝✐❞❛❞❡s ♣r♦❞✉✲ t✐✈❛s ❞♦s ✈ár✐♦s ❛♥♦s✳ ➱ ❛ss✐♠ ♣♦ssí✈❡❧ q✉❛♥t✐✜❝❛r ❛ ✐♥✢✉ê♥❝✐❛ ❞♦ ❢❛❝t♦r ❛♥♦ ♥♦s ♠á①✐♠♦s ❞❛s ❢✉♥çõ❡s ♦❜❥❡❝t✐✈♦✳

❈❛♣ít✉❧♦ ✷

❆♥á❧✐s❡ ❝♦♥❥✉♥t❛ ❞❡ ❘❡❣r❡ssõ❡s

✷✳✶ ◆♦t❛ ❍✐stór✐❝❛

❆ ✐♥✐❝✐❛r ❡st❡ tr❛❜❛❧❤♦ ✈❛♠♦s r❡❢❡r✐r ❜r❡✈❡♠❡♥t❡ ❛ ❤✐stór✐❛ ❞❛ ❆♥á❧✐s❡ ❈♦♥❥✉♥t❛ ❞❡ ❘❡✲ ❣r❡ssõ❡s ▲✐♥❡❛r❡s✳ ▼♦♦❡rs ✭✶✾✷✶✮ ❛♥❞ ❨❛t❡s & ❈♦❝❤r❛♥ ✭✶✾✸✽✮✱ ❢♦r❛♠ ♦s ♣✐♦♥❡✐r♦s ♥♦ ❞❡✲

s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❛ té❝♥✐❝❛✳ ▼❛✐s t❛r❞❡✱ ♥♦s ❛♥♦s s❡ss❡♥t❛✱ ❋✐♥❧❛② & ❲✐❧❦✐♥s♦♥ ✭✶✾✻✸✮ ❡

❊❜❡r❧❤❛rt&❘✉ss❡❧ ✭✶✾✻✻✮✱ ❞❡r❛♠ ♦ s❡✉ ❣r❛♥❞❡ ❝♦♥tr✐❜✉t♦ ♣❛r❛ ❛♣❧✐❝❛çã♦ ❞❛ té❝♥✐❝❛ à ❝♦♠✲

♣❛r❛çã♦ ❞❡ ❝✉❧t✐✈❛r❡s s✉❥❡✐t♦s ❛ ✉♠ ✈❛st♦ ♥ú♠❡r♦ ❞❡ ♥í✈❡✐s ❞❡ ❢❡rt✐❧✐❞❛❞❡✳ ❈♦♠♦ ❝♦♥tr✐❜✉t♦ ♣♦rt✉❣✉ês✱ ●✉s♠ã♦ ✭✶✾✽✺✮✱ ✭✶✾✽✻❛✮ ❡ ✭✶✾✽✻❜✮✱ ♠♦str♦✉ q✉❡ ❛ ♣r❡❝✐sã♦ ❞♦s ❛❥✉st❛♠❡♥t♦s ♠❡❧❤♦r❛✈❛ ❣r❛♥❞❡♠❡♥t❡ s❡ s❡ ❝♦♥s✐❞❡r❛ss❡♠ í♥❞✐❝❡s ❛♠❜✐❡♥t❛✐s ❞✐st✐♥t♦s ♣❛r❛ ♦s ❞✐❢❡r❡♥t❡s ❜❧♦❝♦s✱ ❡♠ ✈❡③ ❞✉♠ ú♥✐❝♦ í♥❞✐❝❡ ♣♦r ❡♥s❛✐♦✳

◆❛ ❞é❝❛❞❛ ❞❡ ♦✐t❡♥t❛✱ t❡♥❞♦ ❝♦♠♦ ❛r❣✉♠❡♥t♦ ♦ ❢❛❝t♦ ❞❡✱ ♥❛ ❆❈❘ ♥ã♦ s❡ ❝♦♥s✐❞❡r❛r❡♠ ✈❛r✲ ✐á✈❡✐s ❛♠❜✐❡♥t❛✐s ❡s♣❡❝í✜❝❛s✱ ❲❡st❝♦tt ✭✶✾✽✻✮ ❡ ▲✐♥ ❡t ❛❧✳ ✭✶✾✽✻✮✱ ❝r✐t✐❝❛r❛♠ ♦ ✉s♦ ❞❡st❛ té❝✲ ♥✐❝❛ ❡♠ ♦♣♦s✐çã♦ ❛ ❇❡❝❦❡r&▲❡♦♥ ✭✶✾✽✽✮ q✉❡ ❝♦♥s✐❞❡r❛♠ s❡r ✉♠❛ ❝rít✐❝❛ ♣♦✉❝♦ ✐♠♣♦rt❛♥t❡✳

❊♠ P♦rt✉❣❛❧ t❡♠♦s ✈ár✐♦s ❛✉t♦r❡s q✉❡ s❡ ❞❡❜r✉ç❛r❛♠ s♦❜r❡ ❡st❡ t❡♠❛✱ sã♦ ❡❧❡s✿ ●✉s♠ã♦ ✭✶✾✽✻❜✮✱ ✭✶✾✾✵✮✱ ●✉s♠ã♦ ❡t ❛❧✳ ✭✶✾✾✶❛✮✱ ✭✶✾✾✶❜✮✱ ✭✶✾✾✷❛✮✱ ✭✶✾✾✷❜✮✱ ✭✶✾✾✸❛✮✱ ✭✶✾✾✸❜✮✱ ✭✶✾✾✺✮✱ ❋❡rr❡✐r❛ ❡t ❛❧✳ ✭✶✾✾✵✮✱ ▼❛çãs ❡t ❛❧✳ ✭✶✾✾✵✮✱ ▼❡①✐❛ ❡t ❛❧✳ ✭✶✾✾✶✮ ❡ ❉✐❛s ✭✷✵✵✵✮✳ ❙❡❣✉✐♥❞♦✲s❡ ●✉s♠ã♦ ✭✶✾✽✺✮ ❡ ✭✶✾✽✻❛✮✱ ❛ ❆❈❘ ❡r❛ ❛♣❧✐❝❛❞❛ ❛ r❡❞❡s ❞❡ ❡♥s❛✐♦s ❡♠ ❜❧♦❝♦s ❝❛s✉❛❧✐③❛❞♦s✱ s❡♥❞♦ ♦s í♥❞✐❝❡s ❛♠❜✐❡♥t❛✐s ❝♦rr❡s♣♦♥❞❡♥t❡s ❛♦s ❞✐❢❡r❡♥t❡s ❜❧♦❝♦s ♠❡❞✐❞♦s ♣❡❧♦s r❡s♣❡❝t✐✈♦s r❡♥❞✐♠❡♥t♦s ♠é❞✐♦s✳ ❊st❡ ♣r♦❝❡❞✐♠❡♥t♦ só s❡ ♣♦❞✐❛ ❛♣❧✐❝❛r q✉❛♥❞♦ s❡ t✐♥❤❛♠ ❜❧♦❝♦s ❝♦♠✲ ♣❧❡t♦s✳ ❆ss✐♠✱ ▼❡①✐❛ ❡t ❛❧✳ ✭✶✾✾✾✮✱ ❝♦♠ ❛ ✐♥tr♦❞✉çã♦ ❞♦s í♥❞✐❝❡s ❛♠❜✐❡♥t❛✐sL2✱ ❛❧❛r❣❛r❛♠

♦ ❝❛♠♣♦ ❞❡ ✉t✐❧✐③❛çã♦ ❞❛ ❆❈❘ ❛♦ ❝❛s♦ ✐♥❝♦♠♣❧❡t♦✳

❉✐❣❜② ✭✶✾✼✾✮ ❡ ◆❣ & ●r✉♥✇❛❧❞ ✭✶✾✾✼✮ ❞❡s❡♥✈♦❧✈❡r❛♠ t❛♠❜é♠ ♠ét♦❞♦s ✐t❡r❛t✐✈♦s ♣❛r❛ ♦

❛❥✉st❛♠❡♥t♦ ❝♦♥❥✉♥t♦ ❞❡ r❡❣r❡ssõ❡s✳

❘❡✜r❛✲s❡ ❛✐♥❞❛✱ ❛ ❞✐ss❡rt❛çã♦ ❞❡ ❞♦✉t♦r❛♠❡♥t♦ ❞❡ P❡r❡✐r❛ ✭✷✵✵✹✮✱ ❡♠ q✉❡ ❛ ❆❈❘ ✉t✐❧✐③❛♥❞♦ í♥❞✐❝❡s ❛♠❜✐❡♥t❛✐s L2✱ é ❞❡s❡♥✈♦❧✈✐❞❛ ❞✉♠❛ ❢♦r♠❛ s✐st❡♠át✐❝❛✳ ❆❧✐ás✱ ♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦