Abstract

The study of random matrices, and in particular the properties of their eigenvalues and eigenvectors, has emerged from applications, first in data analysis and later from statistical models for heavy-nuclei atoms. Recently Random matrix theory has found its numerous application in many other areas, for example, in computational mathematics, communication theory and portfolio theory.
In my talk, I will discuss the limiting laws for the eigenvalues and eigenvectors of ensembles of large n-by-n symmetric random matrices, in the asymptotic limit n tending to infinity. Global and local regimes will be considered. I will also present some applications of random matrix theory.