Exact and Asymptotic Enumeration of Vicious Walkers with a Wall Interaction
by
Christian Krattenthaler
Institut Camille Jordan, Université Claude Bernard Lyon-I

The vicious walker model was introduced by Michael Fisher in Statistical Mechanics in the early 1984s. Many variations of this model have been studied since then. In the particular variation that I shall be interested in there, is an interaction of the walkers with a fixed wall. It was originally proposed by Owczarek, Essam and Brak who found partial results for it. I show how to completely solve the problem of determining the asymptotic behaviour of the corresponding partition function (and of another interesting parameter). In the course of doing that, we shall meet some of my dear friends: determinants, a tableau bijection, and hypergeometric series.

Date received: March 25, 2005