Normal Typicality and Dynamical Typicality for a Random Block-Band Matrix Model

TL;DR

This paper proves normal and dynamical typicality for a random block-band matrix model with block-dependent variances, demonstrating intermediate equilibration times, a novel rigorous result in the field.

Contribution

It introduces a rigorous proof of intermediate equilibration times for a new class of random block-band matrices with block-dependent variances.

Findings

Proves normal and dynamical typicality for the model

Establishes intermediate equilibration times

Builds on concentration estimates for resolvents of Wigner matrices

Abstract

We prove normal typicality and dynamical typicality for a (centered) random block-band matrix model with block-dependent variances. A key feature of our model is that we achieve intermediate equilibration times, an aspect that has not been proven rigorously in any model before. Our proof builds on recently established concentration estimates for products of resolvents of Wigner type random matrices [arXiv:2403.10359] and an intricate analysis of the deterministic approximation.