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 …

A bstract The fine grained energy spectrum of quantum chaotic systems is widely believed to
be described by random matrix statistics. A basic scale in such a system is the energy range …

The many-body localization transition (MBLT) between ergodic and many-body localized
phases in disordered interacting systems is a subject of much recent interest. The statistics …

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 …

The Anderson transition in random graphs has raised great interest, partly out of the hope
that its analogy with the many-body localization (MBL) transition might lead to a better …

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 …

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 …

By varying the disorder realization in the many-body localized (MBL) phase, we investigate
the influence of resonances on spectral properties. The standard theory of the MBL phase is …