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

In contrast with Anderson localization where a genuine localization is observed in real
space, the many-body localization (MBL) problem is much less understood in Hilbert space …

Randomized algorithms for very large matrix problems have received a great deal of
attention in recent years. Much of this work was motivated by problems in large-scale data …

The distinction between level clustering and level repulsion is one of the quantum
analogues of the classical distinction between globally regular and predominantly chaotic …

Random matrix theory is a wide and growing field with a variety of concepts, results, and
techniques and a vast range of applications in mathematics and the related sciences. 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 …

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 …

We reduce a random-band-matrix (RBM) problem to a one-dimensional, nonlinear,
supersymmetric, σ model. This reduction becomes exact in the limit b→∞, b being the …

A numerical study of Anderson transition on random regular graphs (RRGs) with diagonal
disorder is performed. The problem can be described as a tight-binding model on a lattice …

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 …