An interacting particle system with geometric jump rates near a partially reflecting boundary

TL;DR

This paper introduces a new two-dimensional interacting particle system with geometric jumps near a boundary, exhibiting Markovian projections and connections to advanced algebraic structures, with asymptotic behavior linked to well-known stochastic processes.

Contribution

It constructs a novel particle system with boundary interactions, linking algebraic representations to stochastic dynamics and asymptotic analysis.

Findings

Projection to each level is Markovian.

Dynamics match $Sp(inite)$ characters and Pieri formulas.

Asymptotics relate to Discrete Jacobi and Symmetric Pearcey processes.

Abstract

This paper constructs a new interacting particle system on a two--dimensional lattice with geometric jumps near a boundary which partially reflects the particles. The projection to each horizontal level is Markov, and on every level the dynamics match stochastic matrices constructed from pure alpha characters of $Sp(\infty)$, while on every other level they match an interacting particle system from Pieri formulas for $Sp(2r)$. Using a previously discovered correlation kernel, asymptotics are shown to be the Discrete Jacobi and Symmetric Pearcey processes.