Examples of interacting particle systems on $\mathbb{Z}$ as Pfaffian point processes: coalescing branching random walks and annihilating random walks with immigration

Abstract

Two classes of interacting particle systems on $\mathbb{Z}$ are shown to be Pfaffian point processes at fixed times, and for all deterministic initial conditions. The first comprises coalescing and branching random walks, the second annihilating random walks with pairwise immigration. Various limiting Pfaffian point processes on $\mathbb{R}$ are found by diffusive rescaling, including the point set process for the Brownian net.

23 pages

References in corpus (2)

• Extremal laws for the real Ginibre ensemble
• The Brownian net

Cited by in corpus (3)

• Large Deviations For Sticky Brownian Motions
• Asymptotic expansions for a class of Fredholm Pfaffians and interacting particle systems
• Sharp asymptotics for Fredholm Pfaffians related to interacting particle systems and random matrices