Characteristic Polynomials for 1D Random Band Matrices from the Localization Side

Mariya Shcherbina; Tatyana Shcherbina

doi:10.1007/s00220-017-2849-2

Characteristic Polynomials for 1D Random Band Matrices from the Localization Side

Mariya Shcherbina, Tatyana Shcherbina

Mathematics

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

11 Scopus citations

Abstract

We study the special case of n× n 1D Gaussian Hermitian random band matrices, when the covariance of the elements is determined by J=(-W2▵+1)-1. Assuming that the band width W≪n, we prove that the limit of the normalized second mixed moment of characteristic polynomials (as W, n→ ∞) is equal to one, and so it does not coincide with that for GUE. This complements the result of Shcherbina (J Stat Phys 155(3):466–499, 2014) and proves the existence of the expected crossover for 1D Hermitian random band matrices at W∼n on the level of characteristic polynomials.

Original language	English (US)
Pages (from-to)	1009-1044
Number of pages	36
Journal	Communications In Mathematical Physics
Volume	351
Issue number	3
DOIs	https://doi.org/10.1007/s00220-017-2849-2
State	Published - May 1 2017

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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