Book Review: Combinatorics and random matrix theory; Dynamical approach to random matrix theory

Introduction to Random-Matrix Theory

Random-matrix theory gained attention during the 1950s due to work by Eugene Wigner in mathematical physics. Specifically, Wigner wished to describe the general properties of the energy levels (or of their spacings) of highly excited states of heavy nuclei as measured in nuclear reactions (Wigner, 1957). Such a complex nuclear system is represented by an Hermitian operator H (called the Hamilto...

Random Matrix Theory

Random matrix theory is usually taught as a sequence of several graduate courses; we have 16 lectures, so we will give a very brief introduction. Some relevant books for the course: • G. Anderson, A. Guionnet, O. Zeitouni. An introduction to random matrices. [1] • A. Guionnet. Large random matrices: lectures on macroscopic asymptotics. • M. L. Mehta. Random matrices. The study of random matrice...

Random matrix theory

Random matrix theory is now a big subject with applications in many disciplines of science, engineering and finance. This article is a survey specifically oriented towards the needs and interests of a numerical analyst. This survey includes some original material not found anywhere else. We include the important mathematics which is a very modern development, as well as the computational softwa...

Random Matrix Theory

Random matrix theory and number theory

We review some of the connections between Random Matrix Theory and Number Theory. These include modelling the value distributions of the Riemann zeta-function and other L-functions, and the statistical distribution of their zeros. 1.