Geodesic
Asymptotics of Toeplitz, Hankel, and Toeplitz+Hankel determinants with Fisher-Hartwig singularities
Percy Deift1 ; Alexander Its2 ; Igor Krasovsky3
1 Courant Institute of Mathematical Sciences<br/>New York University<br/> 251 Mercer Street<br/> New York, NY 10012
2 Department of Mathematics<br/> Indiana University -- Purdue University Indianapolis<br/>402 N. Blackford St.<br/> Indianapolis, IN 46292-3267
3 Department of Mathematical Sciences<br/> Brunel University<br/> Uxbridge UB8 3PH<br/> United Kingdom
Annals of mathematics, Tome 174 (2011) no. 2, pp. 1243-1299.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We study the asymptotics in $n$ for $n$-dimensional Toeplitz determinants whose symbols possess Fisher-Hartwig singularities on a smooth background. We prove the general nondegenerate asymptotic behavior as conjectured by Basor and Tracy. We also obtain asymptotics of Hankel determinants on a finite interval as well as determinants of Toeplitz+Hankel type. Our analysis is based on a study of the related system of orthogonal polynomials on the unit circle using the Riemann-Hilbert approach.
DOI : 10.4007/annals.2011.174.2.12

Percy Deift 1 ; Alexander Its 2 ; Igor Krasovsky 3

1 Courant Institute of Mathematical Sciences<br/>New York University<br/> 251 Mercer Street<br/> New York, NY 10012
2 Department of Mathematics<br/> Indiana University -- Purdue University Indianapolis<br/>402 N. Blackford St.<br/> Indianapolis, IN 46292-3267
3 Department of Mathematical Sciences<br/> Brunel University<br/> Uxbridge UB8 3PH<br/> United Kingdom 
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     title = {Asymptotics of {Toeplitz,} {Hankel,} and {Toeplitz+Hankel} determinants with {Fisher-Hartwig} singularities},
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Percy Deift; Alexander Its; Igor Krasovsky. Asymptotics of Toeplitz, Hankel, and Toeplitz+Hankel determinants with Fisher-Hartwig singularities. Annals of mathematics, Tome 174 (2011) no. 2, pp. 1243-1299. doi : 10.4007/annals.2011.174.2.12. http://geodesic.mathdoc.fr/articles/10.4007/annals.2011.174.2.12/

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