TY - JOUR

T1 - Characteristic Polynomials for 1D Random Band Matrices from the Localization Side

AU - Shcherbina, Mariya

AU - Shcherbina, Tatyana

N1 - Funding Information:
Tatyana Shcherbina was partially supported by NSF Grant DMS-1128155.
Publisher Copyright:
© 2017, Springer-Verlag Berlin Heidelberg.

PY - 2017/5/1

Y1 - 2017/5/1

N2 - We study the special case of n× n 1D Gaussian Hermitian random band matrices, when the covariance of the elements is determined by J=(-W2▵+1)-1. Assuming that the band width W≪n, we prove that the limit of the normalized second mixed moment of characteristic polynomials (as W, n→ ∞) is equal to one, and so it does not coincide with that for GUE. This complements the result of Shcherbina (J Stat Phys 155(3):466–499, 2014) and proves the existence of the expected crossover for 1D Hermitian random band matrices at W∼n on the level of characteristic polynomials.

AB - We study the special case of n× n 1D Gaussian Hermitian random band matrices, when the covariance of the elements is determined by J=(-W2▵+1)-1. Assuming that the band width W≪n, we prove that the limit of the normalized second mixed moment of characteristic polynomials (as W, n→ ∞) is equal to one, and so it does not coincide with that for GUE. This complements the result of Shcherbina (J Stat Phys 155(3):466–499, 2014) and proves the existence of the expected crossover for 1D Hermitian random band matrices at W∼n on the level of characteristic polynomials.

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U2 - 10.1007/s00220-017-2849-2

DO - 10.1007/s00220-017-2849-2

M3 - Article

AN - SCOPUS:85014288660

SN - 0010-3616

VL - 351

SP - 1009

EP - 1044

JO - Communications In Mathematical Physics

JF - Communications In Mathematical Physics

IS - 3

ER -