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

Tatyana Shcherbina

doi:10.1007/s00220-014-1947-7

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

Tatyana Shcherbina

Mathematics

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29 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 H_N with independent Gaussian entries such that {H_{i j} Hlk} = δ_ikδ _jl J_ij , where J = (−W²Δ+1) ⁻¹.Assuming that W² = N^1+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 language	English (US)
Pages (from-to)	45-82
Number of pages	38
Journal	Communications In Mathematical Physics
Volume	328
Issue number	1
DOIs	https://doi.org/10.1007/s00220-014-1947-7
State	Published - Mar 5 2014

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s00220-014-1947-7

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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{\textquoteright}s asymptotic behavior (as N → ∞) in the bulk of the spectrum coincides with that for the Gaussian Unitary Ensemble.",

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N2 - 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.

AB - 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.

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

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