Foundations and Applications
of Random Matrix Theory

Jacobus Verbaarschot

Stony Brook University, USA

Friday, 27 October 2006, 13:30
Lecture room (Sal) F

Entropy, Symmetries and Universality are essential concepts in statistical physics and field theory. They are also at the foundation of Random Matrix Theory which was introduced by Wigner to describe the statistical properties of nuclear levels without knowledge of the nuclear Hamiltonian. Since then, Random Matrix Theories have found applications in many branches of physics ranging from atomic physics to QCD and quantum gravity and in mathematics in subjects as varied as the Riemann z-function and random permutations. We will review the basic ideas of Random Matrix Theory and explain its relation to classically chaotic motion. Its successes will be illustrated by experimental and theoretical results for spectra of a variety of different physical systems. Recent progress in understanding chiral symmetry in QCD based on ideas from Random Matrix Theory and the theory of disordered systems will be discussed. Finally, the concept of universality is introduced to explain the success of Random Matrix.