# General Contact Process with Rapid Stirring

## TL;DR

This paper investigates the behavior of a contact process with rapid stirring on high-dimensional lattices, focusing on how the critical branching rate changes as the stirring rate becomes very large.

## Contribution

It provides an analysis of the asymptotic behavior of the critical branching rate in the contact process with rapid stirring as the stirring rate tends to infinity.

## Key findings

- Critical branching rate approaches a limit as stirring rate increases
- The model extends classical contact process by incorporating rapid stirring dynamics
- Results contribute to understanding phase transitions in high-dimensional particle systems

## Abstract

We study the limiting behavior of an interacting particle system evolving on the lattice $Z^{d}$ for $d\ge 3$. The model is known as the contact process with rapid stirring. The process starts with a single particle at the origin. Each particle may die, jump to a neighboring site if it is vacant or split. In the case of splitting, one of the offspring takes the place of the parent while the other, the newborn particle, is sent to another site in $Z^{d}$ according to a certain distribution; if the newborn particle lands on an occupied site, its birth is suppressed. We study the asymptotic behavior of the critical branching rate as the jumping rate (also known as the stirring rate) approaches infinity.