Erratum: one dimensional particle systems as extended Pfaffian point processes

Roger Tribe,Siu Yip,Oleg Zaboronski

doi:10.1214/ecp.v20-4302

Abstract

This erratum corrects the statement of the main result in ECP volume 17 paper 40 , which establishes that the mulit-time particle densitites for certain intercating particle systems on the real line are extended Pfaffian point processes.

Highlights

This erratum corrects the statement of the main result in ECP volume 17 paper 40 ([2]) which establishes that the multi-time particle distributions for certain interacting Brownian motions on the real line are extended Pfaffian point processes
Assume that the initial distribution of particles is given by a natural maximal entrance law, which can be constructed as the infinite intensity limit of Poisson initial conditions
Theorem 1.1 of [2] goes on to claim that the extended Pfaffian property holds for instantly coalescing Brownian motions under the same entrance law, but this is false

Summary

Introduction

This erratum corrects the statement of the main result in ECP volume 17 paper 40 ([2]) which establishes that the multi-time particle distributions for certain interacting Brownian motions on the real line are extended Pfaffian point processes. In [2] the following result is proved. Consider a system of annihilating Brownian motions on the real line, where the particles move independently except for instantaneous annihilation when they meet.

Results

Conclusion