An interacting particle system with geometric jump rates near a partially reflecting boundary.(English)Zbl 1384.60098

Summary: 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.

MSC:

 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60G55 Point processes (e.g., Poisson, Cox, Hawkes processes) 82C22 Interacting particle systems in time-dependent statistical mechanics
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