Markov Processes on the Duals to Infinite-Dimensional Classical Lie Groups

TL;DR

This paper develops a four-parameter family of Markov processes that preserve z-measures on the boundaries of branching graphs associated with infinite-dimensional classical Lie groups, extending previous methods.

Contribution

It introduces a new family of Markov dynamics on duals of infinite-dimensional classical Lie groups using the method of intertwiners, generalizing prior constructions.

Findings

Constructed a four-parameter Markov process family

Preserves z-measures on boundary of classical Lie group graphs

Extends previous methods to new group types

Abstract

We construct a four parameter (z, z', a, b) family of Markov dynamics that preserve the z-measures on the boundary of the branching graph for classical Lie groups of type B, C, D. Our guiding principle is the "method of intertwiners" used previously in [7] to construct Markov processes that preserve the zw-measures.