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

Abstract

We consider the asymptotic behavior of the second mixed moment of the characteristic polynomials of the 1D Gaussian band matrices, i.e. of the hermitian matrices $H_n$ with independent Gaussian entries such that $<H_{ij}{H}_{lk}>={\delta }_{ik}{\delta }_{jl}{J}_{ij}$, where $J=(-W^2△+1{)}^{-1}$. Assuming that $W^2=n^{1+\theta }$, $0<\theta <1$, we show that this asymptotic behavior (as $n\to \infty$) in the bulk of the spectrum coincides with those for the Gaussian Unitary Ensemble.

35 pages

References in corpus (1)

• Bulk universality for generalized Wigner matrices

Cited by in corpus (3)

• Some Open Problems in Random Matrix Theory and the Theory of Integrable Systems. II
• Random matrices, log-gases and Holder regularity
• Density of states for GUE, GOE, and interpolating ensembles through supersymmetric approach