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January, 1994 Particle Systems and Reaction-Diffusion Equations
R. Durrett, C. Neuhauser
Ann. Probab. 22(1): 289-333 (January, 1994). DOI: 10.1214/aop/1176988861

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 $\{0, 1\}^S$.

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R. Durrett. C. Neuhauser. "Particle Systems and Reaction-Diffusion Equations." Ann. Probab. 22 (1) 289 - 333, January, 1994. https://doi.org/10.1214/aop/1176988861

Information

Published: January, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0799.60093
MathSciNet: MR1258879
Digital Object Identifier: 10.1214/aop/1176988861

Subjects:
Primary: 60K35
Secondary: 35K35

Rights: Copyright © 1994 Institute of Mathematical Statistics

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Vol.22 • No. 1 • January, 1994
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