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

Mariya Shcherbina, Tatyana Shcherbina

Research output: Contribution to journalArticle

5 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 languageEnglish (US)
Pages (from-to)1233-1260
Number of pages28
JournalJournal of Statistical Physics
Volume164
Issue number6
DOIs
StatePublished - Sep 1 2016

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Keywords

  • Band matrices
  • Density of states
  • Transfer matrix approach

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