The theory of random matrices plays an important role in many areas of pure mathematics
and employs a variety of sophisticated mathematical tools (analytical, probabilistic and …

We consider the eigenvalues and eigenvectors of finite, low rank perturbations of random
matrices. Specifically, we prove almost sure convergence of the extreme eigenvalues and …

We estimate the asymptotics of spherical integrals of real symmetric or Hermitian matrices
when the rank of one matrix is much smaller than its dimension. We show that it is given in …

Random matrix theory has developed in the last few years, in connection with various fields
of mathematics and physics. These notes emphasize the relation with the problem of …

We show that under reasonably general assumptions, the first order asymptotics of the free
energy of matrix models are generating functions for colored planar maps. This is based on …

We consider the asymptotics of $ k $-dimensional spherical integrals when $ k= o (N) $. We
prove that the $ o (N) $-dimensional spherical integrals are approximately the products of $1 …

Large random matrices appear in different fields of mathematics and physics such as
combinatorics, probability theory, statistics, operator theory, number theory, quantum field …

The main result of this paper is a rigorous computation of Wilson loop expectations in
strongly coupled SO (N) lattice gauge theory in the large N limit, in any dimension. The …

Two-Dimensional Quantum Yang–Mills Theory and the Makeenko–Migdal Equations |
SpringerLink Skip to main content Advertisement SpringerLink Account Menu Find a journal …

The $1/N $ expansion is an asymptotic series expansion for certain quantities in large-$ N $
lattice gauge theories. This article gives a rigorous formulation and proof of the $1/N …