# Characteristic polynomials for random band matrices near the threshold

## TL;DR

This paper investigates the behavior of characteristic polynomials of one-dimensional Gaussian Hermitian random band matrices near a critical bandwidth threshold, using transfer matrix methods to analyze the correlation functions.

## Contribution

It extends previous work by analyzing the correlation functions at the critical bandwidth proportional to the square root of matrix size, near the spectral threshold.

## Key findings

- Identifies the behavior of correlation functions near the threshold
- Demonstrates the effectiveness of transfer matrix approach in this regime
- Provides insights into spectral properties of band matrices at critical bandwidths

## 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 $J=(-W^2\triangle+1)^{-1}$. Applying the transfer matrix approach, we study the case when the bandwidth $W$ is proportional to the threshold $\sqrt{n}$