High values of disorder-generated multifractals and logarithmically correlated processes

TL;DR

This paper explores the extreme values of disorder-generated multifractals and their connection to logarithmically correlated processes, providing analytical insights and numerical investigations into multifractal eigenvectors in random matrix ensembles.

Contribution

It offers a new analytical approach to understanding high-value statistics of multifractals and reveals hidden logarithmic correlations in the Ruijsenaars-Schneider ensemble.

Findings

Analytical calculation of logarithmic correlations in multifractal eigenvectors

Numerical evidence supporting the connection between multifractality and logarithmic correlations

Identification of high-value statistics in disorder-generated multifractals

Abstract

In the introductory section of the article we give a brief account of recent insights into statistics of high and extreme values of disorder-generated multifractals following a recent work by the first author with P. Le Doussal and A. Rosso (FLR) employing a close relation between multifractality and logarithmically correlated random fields. We then substantiate some aspects of the FLR approach analytically for multifractal eigenvectors in the Ruijsenaars-Schneider ensemble (RSE) of random matrices introduced by E. Bogomolny and the second author by providing an ab initio calculation that reveals hidden logarithmic correlations at the background of the disorder-generated multifractality. In the rest we investigate numerically a few representative models of that class, including the study of the highest component of multifractal eigenvectors in the Ruijsenaars-Schneider ensemble.