On convergence of dynamics of hopping particles to a birth-and-death process in continuum

TL;DR

This paper demonstrates that certain birth-and-death processes in continuum can be obtained as scaling limits of interacting hopping particle dynamics, linking Kawasaki and Glauber dynamics.

Contribution

It establishes a rigorous connection between Kawasaki and Glauber dynamics through a scaling limit in continuum particle systems.

Findings

Birth-and-death processes can be derived as limits of hopping particle dynamics.

A mathematical framework for the convergence of these processes is provided.

The results bridge two important types of stochastic dynamics in continuum.

Abstract

We show that some classes of birth-and-death processes in continuum (Glauber dynamics) may be derived as a scaling limit of a dynamics of interacting hopping particles (Kawasaki dynamics)