Workshop: Discrete Whittaker processes

Speaker
O’Connell, University College Dublin

Abstract
I will discuss a Markov chain on reverse plane partitions (of a given shape) which is closely related to fundamental Whittaker functions and the Toda lattice. This process has non-trivial Markovian projections and a unique entrance law starting from the reverse plane partition with all entries equal to plus infinity. I will also outline some connections with imaginary exponential functionals of Brownian motion, a semi-discrete polymer model with purely imaginary disorder, interacting corner growth processes and discrete delta-Bose gas, and hitting probabilities for some low rank examples.