Schur dynamics of the Schur processes

TL;DR

This paper develops Markov chains that preserve Schur processes, enabling exact sampling of skew plane partitions and modeling deterministic flows on infinite Gelfand-Tsetlin schemes related to the infinite-dimensional unitary group.

Contribution

It introduces new Markov chain constructions that maintain Schur process structures, facilitating exact sampling and analysis of infinite-dimensional representation spaces.

Findings

Exact sampling algorithm for skew plane partitions with arbitrary back wall

Construction of Markov chains on infinite Gelfand-Tsetlin schemes

Representation of flows on extreme characters of the infinite-dimensional unitary group

Abstract

We construct discrete time Markov chains that preserve the class of Schur processes on partitions and signatures. One application is a simple exact sampling algorithm for q^{volume}-distributed skew plane partitions with an arbitrary back wall. Another application is a construction of Markov chains on infinite Gelfand-Tsetlin schemes that represent deterministic flows on the space of extreme characters of the infinite-dimensional unitary group.