Interacting Diffusions on Positive Definite Matrices
[HYBRID WORKSHOP] Integrable Structures in Random Matrix Theory and Beyond October 18, 2021 - October 22, 2021
Location: MSRI: Simons Auditorium, Online/Virtual
Whittaker functions of matrix argument
Diffusion processes with one-sided interactions
Non-Abelian Toda lattice
We consider systems of Brownian particles in the space of positive definite matrices, which evolve independently apart from some simple interactions. We give examples of such processes which have an integrable structure. These are related to K-Bessel functions of matrix argument and multivariate generalisations of these functions. The latter are eigenfunctions of a particular quantisation of the non-Abelian Toda lattice.