High values of disorder-generated multifractals and logarithmically correlated processes

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.