Eigenfunction entropy and spectral compressibility for critical random matrix ensembles

TL;DR

This paper conjectures a simple relationship between eigenfunction information dimension and spectral compressibility in critical random matrix models, supported by numerical and perturbation analyses.

Contribution

It introduces a conjecture linking eigenfunction information dimension and spectral compressibility in critical random matrix ensembles.

Findings

Proposes the relation chi + D_1/d = 1 for certain models

Supports the conjecture with numerical evidence

Uses perturbation series arguments

Abstract

Based on numerical and perturbation series arguments we conjecture that for certain critical random matrix models the information dimension of eigenfunctions D_1 and the spectral compressibility chi are related by the simple equation chi+D_1/d=1, where d is the system dimensionality.