We review selected advances in the theoretical understanding of complex quantum many-
body systems with regard to emergent notions of quantum statistical mechanics. We cover …

The classical random walk formalism plays an important role in a wide range of applications.
Its quantum counterpart, the quantum walk, is proposed as an important theoretical model …

This book provides an introduction to the mathematical theory of disorder effects on quantum
spectra and dynamics. Topics covered range from the basic theory of spectra and dynamics …

Higher order tensor inversion is possible for even order. This is due to the fact that a tensor
group endowed with the contracted product is isomorphic to the general linear group of …

This monograph contains the notes of lectures I gave in Saint Flour Probability Summer
School in July 2016. The two other courses were given by Paul Bourgade and by Scott …

Many-body localization is a striking mechanism that prevents interacting quantum systems
from thermalizing. The absence of thermalization behavior manifests itself, for example, in a …

We study the thermalizing properties of the mass-deformed Sachdev-Ye-Kitaev model, in a
regime of parameters where the eigenstates are ergodically extended over just portions of …

We consider a Hamiltonian given by the Laplacian plus a Bernoulli potential on the two
dimensional lattice. We prove that, for energies sufficiently close to the edge of the spectrum …

These are lecture notes based on three lectures given by Antonello Scardicchio at the
December 2016 Topical School on Many-Body-Localization organized by the Statistical …

These lectures present some basic ideas and techniques in the spectral analysis of lattice
Schrödinger operators with disordered potentials. In contrast to the classical Anderson tight …