Limiting directions for random walks in affine Weyl groups
The multispecies totally asymmetric simple exclusion process (MTASEP) is an interacting particle system defined on a finite one-dimensional integer lattice with periodic boundary conditions. The exact stationary distribution of this Markov process was described by P. Ferrari and J. Martin using multiclass M/M/1 queues. Recently, T. Lam considered a random walk on the alcoves of an affine Weyl group conditioned never to cross the same hyperplane twice. He proved that the limiting direction of this walk exists almost surely, and conjectured a formula for it for \tilde{A}_n. I will describe joint work with S. Linusson, where we solved this conjecture by computing this limiting direction as certain correlations of the MTASEP.

Time permitting, I will describe extensions of our work for the affine Weyl group \tilde{C}_n. This involves the study of correlations in a multispecies exclusion process with open boundaries (i.e., allowing the entry and exit of particles). Here, we have also computed this limiting direction building on existing work of C. Arita, in joint work with E. Aas, S. Linusson and S. Potka.
Date: 21 May 2018, 12:00 (Monday, 5th week, Trinity 2018)
Venue: Mathematical Institute, Woodstock Road OX2 6GG
Speaker: Arvind Ayyer (Indian Institute of Science, Bangalore)
Organising department: Department of Statistics
Organisers: Christina Goldschmidt (Department of Statistics, University of Oxford), James Martin (Department of Statistics, University of Oxford)
Part of: Probability seminar
Booking required?: Not required
Audience: Public
Editors: Christina Goldschmidt, James Martin