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

Kuan, Jeffrey

Electron. Commun. Probab. 21, Paper No. 76, 15 p. (2016).

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

Keywords:

hard-edge; reflecting boundary; Pearcey process; symplectic