Asymptotics of Toeplitz, Hankel, and Toeplitz+Hankel determinants with Fisher-Hartwig singularities

By Percy Deift, Alexander Its, I. Krasovsky. 2009

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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 non-degenerate 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.

Subfields: Applied Mathematics, Discrete Mathematics and Combinatorics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d07f173de639d547e7795830e8ff11059cb72e75

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In Applied Mathematics

1. Pasquale Calabrese
2. M. Fagotti
3. F. Essler

In Discrete Mathematics and Combinatorics

1. Pasquale Calabrese
2. M. Fagotti
3. F. Essler

In Statistics and Probability

1. Pasquale Calabrese
2. M. Fagotti
3. F. Essler
4. Ivan Corwin
5. Alexei Borodin
6. K. Takeuchi

Citations in the corpus

• Quantum quenches in the transverse field Ising chain: II. Stationary state properties (2012, methodology): “nant of Toeplitz matrices, such as Szego’s lemma, the Fisher-Hartwig conjecture, and generalizations thereof (the results we need in the following are summarized inAppendix Aand are taken from Refs. [68,69,70,71]). To apply these theorems it is useful to change variable as z= eik, so that the symbol”