Transfer Matrix Approach to 1d Random Band Matrices: Density of States

Mariya Shcherbina; Tatyana Shcherbina

doi:10.1007/s10955-016-1593-x

Transfer Matrix Approach to 1d Random Band Matrices: Density of States

Mariya Shcherbina
, Tatyana Shcherbina

Mathematics

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

14 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 the matrix J=(-W2▵+1)-1. Assuming that n≥ CWlog W≫ 1 , we prove that the averaged density of states coincides with the Wigner semicircle law up to the correction of order W^{- 1}.

Original language	English (US)
Pages (from-to)	1233-1260
Number of pages	28
Journal	Journal of Statistical Physics
Volume	164
Issue number	6
DOIs	https://doi.org/10.1007/s10955-016-1593-x
State	Published - Sep 1 2016

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

Keywords

Band matrices
Density of states
Transfer matrix approach

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10.1007/s10955-016-1593-x

Cite this

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abstract = "We study the special case of n× n 1D Gaussian Hermitian random band matrices, when the covariance of the elements is determined by the matrix J=(-W2▵+1)-1. Assuming that n≥ CWlog W≫ 1 , we prove that the averaged density of states coincides with the Wigner semicircle law up to the correction of order W- 1.",

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author = "Mariya Shcherbina and Tatyana Shcherbina",

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N2 - We study the special case of n× n 1D Gaussian Hermitian random band matrices, when the covariance of the elements is determined by the matrix J=(-W2▵+1)-1. Assuming that n≥ CWlog W≫ 1 , we prove that the averaged density of states coincides with the Wigner semicircle law up to the correction of order W- 1.

AB - We study the special case of n× n 1D Gaussian Hermitian random band matrices, when the covariance of the elements is determined by the matrix J=(-W2▵+1)-1. Assuming that n≥ CWlog W≫ 1 , we prove that the averaged density of states coincides with the Wigner semicircle law up to the correction of order W- 1.

KW - Band matrices

KW - Density of states

KW - Transfer matrix approach

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UR - https://www.scopus.com/pages/publications/84982851741#tab=citedBy

U2 - 10.1007/s10955-016-1593-x

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M3 - Article

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IS - 6

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Transfer Matrix Approach to 1d Random Band Matrices: Density of States

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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