Asymptotic formulas for determinants of a special class of Toeplitz + Hankel matrices

2016/03/01 by Estelle Basor, Estelle L. Basor, Torsten Ehrhardt +2 · 2 citations
Mathematics · #47B35 #Advanced Algebra and Geometry #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical functions and polynomials #Random Matrices and Applications #math.FA #msc:47B35

paper · pdf · doi:10.48550/arxiv.1603.00506

arxiv created 2016/03/01 · openalex publication_date 2016/03/01 · arxiv updated 2016/03/03 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We compute the asymptotics of the determinants of certain n× n Toeplitz + Hankel matrices T_n(a)+H_n(b) as n→∞ with symbols of Fisher-Hartwig type. More specifically we consider the case where a has zeros and poles and where b is related to a in specific ways. Previous results of Deift, Its and Krasovsky dealt with the case where a is even. We are generalizing this in a mild way to certain non-even symbols.

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• Partition functions of two-dimensional Coulomb gases with circular root- and jump-type singularities
• A Riemann-Hilbert Approach to Asymptotic Analysis of Toeplitz+Hankel Determinants

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