Characteristic Polynomials for Random Band Matrices Near the Threshold

Tatyana Shcherbina

doi:10.1007/s10955-020-02567-3

Characteristic Polynomials for Random Band Matrices Near the Threshold

Tatyana Shcherbina

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

The paper continues (Shcherbina and Shcherbina in Commun Math Phys 351:1009–1044, 2017); Shcherbina in Commun Math Phys 328:45–82, 2014) which study the behaviour of second correlation function of characteristic polynomials of the special case of n× n one-dimensional Gaussian Hermitian random band matrices, when the covariance of the elements is determined by the matrix J=(-W2▵+1)-1. Applying the transfer matrix approach, we study the case when the bandwidth W is proportional to the threshold n.

Original language	English (US)
Pages (from-to)	920-944
Number of pages	25
Journal	Journal of Statistical Physics
Volume	179
Issue number	4
DOIs	https://doi.org/10.1007/s10955-020-02567-3
State	Published - May 1 2020

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Keywords

Band matrices
Characteristic polynomials
Transfer matrices

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10.1007/s10955-020-02567-3

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abstract = "The paper continues (Shcherbina and Shcherbina in Commun Math Phys 351:1009–1044, 2017); Shcherbina in Commun Math Phys 328:45–82, 2014) which study the behaviour of second correlation function of characteristic polynomials of the special case of n× n one-dimensional Gaussian Hermitian random band matrices, when the covariance of the elements is determined by the matrix J=(-W2▵+1)-1. Applying the transfer matrix approach, we study the case when the bandwidth W is proportional to the threshold n.",

keywords = "Band matrices, Characteristic polynomials, Transfer matrices",

author = "Tatyana Shcherbina",

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AB - The paper continues (Shcherbina and Shcherbina in Commun Math Phys 351:1009–1044, 2017); Shcherbina in Commun Math Phys 328:45–82, 2014) which study the behaviour of second correlation function of characteristic polynomials of the special case of n× n one-dimensional Gaussian Hermitian random band matrices, when the covariance of the elements is determined by the matrix J=(-W2▵+1)-1. Applying the transfer matrix approach, we study the case when the bandwidth W is proportional to the threshold n.

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KW - Transfer matrices

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Characteristic Polynomials for Random Band Matrices Near the Threshold

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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