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

Abstract

This paper constructs a new interacting particle system on $\mathbb{Z} _{\geq 0}\times \mathbb{Z} _+$ with geometric jumps near the boundary $\{0\}\times \mathbb{Z} _+$ 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.