  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.

Disordered Systems and Neural Networks;Statistical Mechanics