# Transfer operator approach to 1d random band matrices

## TL;DR

This paper applies the transfer operator method to analyze spectral properties of 1d random band matrices, revealing a phase transition at a critical bandwidth threshold.

## Contribution

It introduces a transfer operator framework to study spectral characteristics and identifies a phase transition at the bandwidth threshold in 1d random band matrices.

## Key findings

- Spectral characteristics change at the bandwidth W=N^{1/2}
- Transfer operator spectral properties explain the phase transition
- Different spectral regimes are characterized by the transfer operator analysis

## Abstract

We discuss an application of the transfer operator approach to the analysis of the different spectral characteristics of 1d random band matrices (correlation functions of characteristic polynomials, density of states, spectral correlation functions). We show that when the bandwidth $W$ crosses the threshold $W=N^{1/2}$, the model has a kind of phase transition (crossover), whose nature can be explained by the spectral properties of the transfer operator.