Characteristic polynomials for random band matrices near the threshold

Abstract

The paper continues previous works which study the behavior of second correlation function of characteristic polynomials of the special case of $n\times n$ one-dimensional Gaussian Hermitian random band matrices, when the covariance of the elements is determined by the matrix $J=(-W^2△+1{)}^{-1}$. Applying the transfer matrix approach, we study the case when the bandwidth $W$ is proportional to the threshold $\sqrt{n}$

21p

References in corpus (4)

• Anderson Transitions
• Characteristic polynomials for 1D random band matrices from the localization side
• On the Second-Order Correlation Function of the Characteristic Polynomial of a Hermitian Wigner Matrix
• On the correlation functions of the characteristic polynomials of the sparse hermitian random matrices

Cited by in corpus (2)

• Optimal Lower Bound on the Least Singular Value of the Shifted Ginibre Ensemble
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