On the second mixed moment of the characteristic polynomials of 1D band matrices

Tatyana Shcherbina

Research output: Contribution to journalArticle

17 Scopus citations

Abstract

We consider the asymptotic behavior of the second mixed moment of the characteristic polynomials of 1D Gaussian band matrices, i.e., of the Hermitian N × N matrices HN with independent Gaussian entries such that {Hi j Hlk} = δikδ jl Jij , where J = (−W2Δ+1) −1.Assuming that W2 = N1+θ, 0 < θ ≤ 1, we showthat themoment’s asymptotic behavior (as N → ∞) in the bulk of the spectrum coincides with that for the Gaussian Unitary Ensemble.

Original languageEnglish (US)
Pages (from-to)45-82
Number of pages38
JournalCommunications In Mathematical Physics
Volume328
Issue number1
DOIs
StatePublished - Mar 5 2014

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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