In any medium there are fluctuations due to temperature or due to the quantum nature of its
constituents. If a material body is immersed into such a medium, its shape and the properties …

Random matrix theory has found many applications in physics, statistics and engineering
since its inception. Although early developments were motivated by practical experimental …

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 …

These expository notes are centered around the circular law theorem, which states that the
empirical spectral distribution of an× n random matrix with iid entries of variance 1/n tends to …

The following sections are included: Preliminaries Principles of Statistical Mechanics
Thermodynamic limit Equivalence of Gibbs ensembles Phase transitions Order parameter …

Sompolinski and Zippelius (1981) propose the study of dynamical systems whose invariant
measures are the Gibbs measures for (hard to analyze) statistical physics models of interest …

We derive concentration inequalities for functions of the empirical measure of eigenvalues
for large, random, self adjoint matrices, with not necessarily Gaussian entries. The results …

We study the normalized trace gn (z)= n− 1 tr (H− zI)− 1 of the resolvent of n× n real
symmetric matrices H=[(1+ δ jk) W jk√ n] j, k= 1 n assuming that their entries are …

We establish bounds on the spectral radii for a large class of sparse random matrices, which
includes the adjacency matrices of inhomogeneous Erdős–Rényi graphs. Our error bounds …

We study Wigner ensembles of symmetric random matrices A=(a ij), i, j= 1,..., n with matrix
elements a ij, i≤ j being independent symmetrically distributed random variables a_ ij= a …