Let n be a large integer and Mn be an n by n complex matrix whose entries are independent
(but not necessarily identically distributed) discrete random variables. The main goal of this …

Abstract We study continuous Anderson Hamiltonians with non-degenerate single site
probability distribution of bounded support, without any regularity condition on the single site …

We give a widely self-contained introduction to the mathematical theory of the Anderson
model. After defining the Anderson model and determining its almost sure spectrum, we …

We present and discuss the many results obtained concerning a famous limit theorem, the
local limit theorem, which has many interfaces, with Number Theory notably, and for which …

A technically convenient signature of Anderson localization is exponential decay of the
fractional moments of the Green function within appropriate energy ranges. We consider a …

The aim of this paper is to study a dimorphic property associated with two different sums of
identically independent Bernoulli random variables having two different families of …

For fa weighted voting scheme used by n voters to choose between two candidates, the n
Shapley–Shubik Indices (or Shapley values) of f measure how much control each voter can …

We show that the Bernoulli part extraction method can be used to obtain approximate forms
of the local limit theorem for sums of independent lattice valued random variables, with …

This book is about rigorous results on localization in multi-particle interactive Anderson
models, mostly on a cubic lattice Zd of dimension d 1. The book emerged in the wake of …

We prove that at least $\Omega (n^{0.51}) $ hyperplanes are needed to slice all edges of the
$ n $-dimensional hypercube. We provide a couple of applications: lower bounds on the …