Jacobus Verbaarschot

SUNY at Stony Brook

Title: Random Matrix Theory: Parameterizing the Unknown

Abstract: Entropy, Symmetries and Universality have been important concepts in modern physics which, when combined together, complement our lack of knowledge of a system. 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 all branches of physics ranging from atomic physics to QCD and quantum gravity.

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 Theory in parameterizing our ignorance of a system.