One dimensional annihilating particle systems as extended Pfaffian point processes

TL;DR

This paper proves that the multi-time distributions of annihilating Brownian motions under a maximal entrance law form extended Pfaffian point processes, revealing a new mathematical structure for these particle systems.

Contribution

It establishes that annihilating Brownian motions' multi-time distributions are extended Pfaffian point processes, a novel connection in stochastic particle systems.

Findings

Multi-time distributions are extended Pfaffian point processes.

Provides a mathematical framework for analyzing annihilating Brownian motions.

Enhances understanding of particle system structures.

Abstract

We prove that the multi-time particle distributions for annihilating Brownian motions, under the maximal entrance law on the real line, are extended Pfaffian point processes