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Interacting Diffusions on Positive Definite Matrices

[HYBRID WORKSHOP] Integrable Structures in Random Matrix Theory and Beyond October 18, 2021 - October 22, 2021

October 19, 2021 (10:20 AM PDT - 11:10 AM PDT)
Speaker(s): Neil O'Connell (University College Dublin)
Location: MSRI: Simons Auditorium, Online/Virtual
Tags/Keywords
  • Whittaker functions of matrix argument

  • Diffusion processes with one-sided interactions

  • Intertwining relations

  • Non-Abelian Toda lattice

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Abstract

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.

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