Information functionals and the notion of (un)certainty: RMT - inspired case

TL;DR

This paper explores how information functionals measure the randomness of probability distributions, focusing on eigenvalue spacing in random matrix theory and analyzing the 'minimum information' assumption to understand disorder and organization.

Contribution

It provides a detailed analysis of the 'minimum information' assumption in the context of eigenvalue distributions, linking information theory with random matrix theory.

Findings

Eigenvalue spacing distributions vary in their degree of randomness.

The 'minimum information' assumption influences the interpretation of eigenvalue statistics.

Information functionals effectively quantify the level of order or disorder in spectral data.

Abstract

Information functionals allow to quantify the degree of randomness of a given probability distribution, either absolutely (through min/max entropy principles) or relative to a prescribed reference one. Our primary aim is to analyze the "minimum information" assumption, which is a classic concept (R. Balian, 1968) in the random matrix theory. We put special emphasis on generic level (eigenvalue) spacing distributions and the degree of their randomness, or alternatively - information/organization deficit.