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

2016/03/01 by Estelle Basor, Torsten Ehrhardt, Basor, Estelle L. +1 · 1 citation
Mathematics · #47B35 #Advanced Algebra and Geometry #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical functions and polynomials #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1603.00506

openalex publication_date 2016/03/01 · 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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