# Integrability and exact results for general \beta 0

#### by Peter Forrester

Institution: The University of Melbourne
Date: Thu 14th June 2007
Time: 3:15 PM
Location: Russell Love Theatre, Richard Berry building

Abstract: With Delta denoting the Vandermonde product of eigenvalue differences, classical random matrix theory gives rise to eigenvalue PDFs of the form of a classical weight function times Delta to the power of beta, for beta = 1,2 or 4. In recent years random tridiagonal and unitary Hessenberg matrices have been identified which realize these PDFs for general \beta 0. Although not possessing determinant and Pfaffian structures characteristic of beta = 1,2 and 4, there are nonetheless underlying integrable structures, and these lead to the exact evaluation of correlations and distribution functions, as will be explained.

For More Information: Dr Jan de Gier Phone: +61 3 8344 6603 J.Degier@ms.unimelb.edu.au