We review the development of random-matrix theory (RMT) during the last fifteen years. We
emphasize both the theoretical aspects, and the application of the theory to a number of …

The article reviews recent developments in the theory of fluctuations and correlations of
energy levels and eigenfunction amplitudes in diffusive mesoscopic samples. Various …

Motivated by the problem of many-body localization and the recent numerical results for the
level and eigenfunction statistics on the random regular graphs, a generalization of the …

The interplay between non-Hermiticity and disorder plays an important role in condensed
matter physics. Here, we report the universal critical behaviors of the Anderson transitions …

This review is intended to give a pedagogical and unified view on the subject of the statistics
and scaling of physical quantities in disordered electron systems at very low temperatures …

Statistics of the inverse participation ratio (IPR) at the critical point of the localization
transition is studied numerically for the power-law random banded matrix model. It is shown …

We develop a novel analytical approach to the problem of single particle localization in
infinite dimensional spaces such as Bethe lattice and random regular graph models. The …

Critical fluctuations of wave functions and energy levels at the Anderson transition are
studied for the family of the power-law random banded matrix ensembles. It is shown that the …

Résumé La formalisation non standard, due à P. Cartier et Y. Perrin, des oscillations rapides
fournit un cadre mathématique adéquat pour de nouvelles techniques d'estimation non …

An overview of the random network model invented by Chalker and Coddington, and its
generalizations, is provided. After a short introduction into the physics of the Integer …