Some Examples of Dynamics for Gelfand Tsetlin Patterns

TL;DR

This paper explores stochastic processes within the Gelfand Tsetlin cone, highlighting independent component dynamics with interactions, and provides examples related to conditioned Markov processes, last passage times, and exclusion processes.

Contribution

It introduces specific examples of Gelfand Tsetlin processes with unique interaction mechanisms and analyzes their properties and couplings.

Findings

Components evolve independently with blocking and pushing interactions

Provides couplings to conditioned Markov processes and exclusion processes

Includes an example of a cone-valued process constrained by a wall at the origin

Abstract

We give examples of stochastic processes in the Gelfand Tsetlin cone in which each component evolves independently apart from a blocking and pushing interaction. The processes give couplings to certain conditioned Markov processes, last passage times and asymetric exclusion processes. An example of a cone valued process whose components cannot escape past a wall at the origin is also considered.