General Contact Process with Rapid Stirring

2019/01/30 by Segev Shlomov, Shlomov, Segev, Leonid Mytnik +1
Mathematics · Physics and Astronomy · #82C22 #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1901.10775

openalex publication_date 2019/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the limiting behavior of an interacting particle system evolving on the lattice Z^d for d≥ 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.

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