Colloquium, 11/16/2012

UAHuntsville Distinguished Lecture Series

Asymmetric Simple Exclusion Process: Bethe Ansatz Approach to the Kolmogorov Equations and Limit Theorems

Craig A. Tracy

Distinguished Professor
Department of Mathematics
University of California, Davis

3:00 Friday, 16 November 2012
107 Shelby Center

 Abstract

We explain how some old ideas of Hans Bethe (called Bethe Ansatz) lead to an explicit formula for the transition probability for the N-particle ASEP. We then discuss the limit as N goes to infinity, and associated limit theorems. Connections with the Kardar-Parisi-Zhang (KPZ) equation will be presented.

Biographical Sketch

Professor Craig Arnold Tracy is an American mathematician, known for his contributions to mathematical physics and probability theory.  Born in United Kingdom, he moved as infant to Missouri where he grew up and obtained a B.Sc.
in physics from University of Missouri (1967). He studied as a Woodrow Wilson Fellow at the Stony Brook University where he obtained a Ph.D. on the thesis entitled Spin-Spin Scale-Functions in the Ising and XY-Models (1973) advised by Barry
M. McCoy, in which (also jointly with Tai Tsun Wu and Eytan Barouch) he studied Painlevé functions in exactly solvable statistical mechanical models. He then was on the faculty of Dartmouth College (1978–84) before joining University of California, Davis (1984) where he is now a distinguished professor. With Harold Widom he worked on the asymptotic analysis of Toeplitz determinants and their various operator theoretic generalizations. This work gave them both the George Pólya and the Norbert Wiener prizes, and the Tracy–Widom distribution is named after them.