Universality of the second mixed moment of the characteristic polynomials of the 1D band matrices: Real symmetric case

Tatyana Shcherbina

doi:10.1063/1.4922621

Universality of the second mixed moment of the characteristic polynomials of the 1D band matrices: Real symmetric case

Tatyana Shcherbina

Mathematics

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8 Scopus citations

Abstract

We prove that the asymptotic behavior of the second mixed moment of the characteristic polynomials of the N × N 1D Gaussian real symmetric band matrices with the width of the band W ≫ N^1/2 coincides with those for the Gaussian orthogonal ensemble. Here, we adapt the approach of Shcherbina [Commun. Math. Phys. 328, 45-82 (2014)], where the Hermitian case was considered.

Original language	English (US)
Article number	063303
Journal	Journal of Mathematical Physics
Volume	56
Issue number	6
DOIs	https://doi.org/10.1063/1.4922621
State	Published - Jun 2015

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.4922621

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title = "Universality of the second mixed moment of the characteristic polynomials of the 1D band matrices: Real symmetric case",

abstract = "We prove that the asymptotic behavior of the second mixed moment of the characteristic polynomials of the N × N 1D Gaussian real symmetric band matrices with the width of the band W ≫ N1/2 coincides with those for the Gaussian orthogonal ensemble. Here, we adapt the approach of Shcherbina [Commun. Math. Phys. 328, 45-82 (2014)], where the Hermitian case was considered.",

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AB - We prove that the asymptotic behavior of the second mixed moment of the characteristic polynomials of the N × N 1D Gaussian real symmetric band matrices with the width of the band W ≫ N1/2 coincides with those for the Gaussian orthogonal ensemble. Here, we adapt the approach of Shcherbina [Commun. Math. Phys. 328, 45-82 (2014)], where the Hermitian case was considered.

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Universality of the second mixed moment of the characteristic polynomials of the 1D band matrices: Real symmetric case

Abstract

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