The physics of Anderson transitions between localized and metallic phases in disordered
systems is reviewed. The term “Anderson transition” is understood in a broad sense …

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

The article reviews the physics of Anderson localization on random regular graphs (RRG)
and its connections to many-body localization (MBL) in disordered interacting systems …

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 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 …

We develop a semi-quantitative theory of electron pairing and resulting superconductivity in
bulk “poor conductors” in which Fermi energy EF is located in the region of localized states …

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 …

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 …

The isolated one-dimensional Heisenberg model with static random magnetic fields has
become paradigmatic for the analysis of many-body localization. Here, we study the …

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 …