Microscopic selection principle for a diffusion-reaction equation

Maury D Bramson, P. Calderoni, A. De Masi, P. Ferrari, J. Lebowitz, R. H. Schonmann

Research output: Contribution to journalArticlepeer-review

45 Scopus citations

Abstract

We consider a model of stochastically interacting particles on ℤ, where each site is assumed to be empty or occupied by at most one particle. Particles jump to each empty neighboring site with rate γ/2 and also create new particles with rate 1/2 at these sites. We show that as seen from the rightmost particle, this process has precisely one invariant distribution. The average velocity of this particle V(γ) then satisfies γ-1/2V(γ)→ {Mathematical expression} as γ→∞. This limit corresponds to that of the macroscopic density obtained by rescaling lengths by a factor γ1/2 and letting γ→∞. This density solves the reaction-diffusion equation {Mathematical expression}, and under Heaviside initial data converges to a traveling wave moving at the same rate {Mathematical expression}.

Original languageEnglish (US)
Pages (from-to)905-920
Number of pages16
JournalJournal of Statistical Physics
Volume45
Issue number5-6
DOIs
StatePublished - Dec 1 1986

Keywords

  • Diffusion-reaction equation

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