Tagged particle processes and their non-explosion criteria

TL;DR

This paper derives tagged particle processes from interacting Brownian motions, establishes non-explosion criteria, and proves the quasi-regularity of related Dirichlet forms, advancing understanding of particle dynamics in stochastic environments.

Contribution

It introduces new criteria for non-explosion and proves quasi-regularity of Dirichlet forms for tagged particles, building on previous invariance principle results.

Findings

Established non-explosion criteria for tagged particle processes.

Proved quasi-regularity of Dirichlet forms for the environment seen from the tagged particle.

Connected the results to invariance principles in interacting Brownian motions.

Abstract

We give a derivation of tagged particle processes from unlabeled interacting Brownian motions. We give a criteria of the non-explosion property of tagged particle processes. We prove the quasi-regularity of Dirichlet forms describing the environment seen from the tagged particle, which were used in previous papers to prove the invariance principle of tagged particles of interacting Brownian motions.