The Annals of Probability

Particle Systems and Reaction-Diffusion Equations

R. Durrett and C. Neuhauser

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Abstract

In this paper we will consider translation invariant finite range particle systems with state space $\{0, 1,\ldots,\kappa - 1\}^S$ with $S = \varepsilon \mathbb{Z}^d$. De Masi, Ferrari and Lebowitz have shown that if we introduce stirring at rate $\varepsilon^{-2}$, then the system converges to the solution of an associated reaction diffusion equation. We exploit this connection to prove results about the existence of phase transitions when the stirring rate is large that apply to a wide variety of examples with state space $\{0, 1\}^S$.

Article information

Source
Ann. Probab., Volume 22, Number 1 (1994), 289-333.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176988861

Digital Object Identifier
doi:10.1214/aop/1176988861

Mathematical Reviews number (MathSciNet)
MR1258879

Zentralblatt MATH identifier
0799.60093

JSTOR
links.jstor.org

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 35K35: Initial-boundary value problems for higher-order parabolic equations

Keywords
Contact process sexual reproduction model mean field limit theorem hydrodynamic limit reaction diffusion equation metastability

Citation

Durrett, R.; Neuhauser, C. Particle Systems and Reaction-Diffusion Equations. Ann. Probab. 22 (1994), no. 1, 289--333. doi:10.1214/aop/1176988861. https://projecteuclid.org/euclid.aop/1176988861


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