PARTICLE-SYSTEMS AND REACTION-DIFFUSION EQUATIONS

被引：75

作者：

DURRETT, R ^{[1
]}

NEUHAUSER, C ^{[1
]}

机构：

[1] UNIV SO CALIF,DEPT MATH,LOS ANGELES,CA 90089

来源：

ANNALS OF PROBABILITY | 1994年 / 22卷 / 01期

关键词：

CONTACT PROCESS; SEXUAL REPRODUCTION MODEL; MEAN FIELD LIMIT THEOREM; HYDRODYNAMIC LIMIT; REACTION DIFFUSION EQUATION; METASTABILITY;

D O I：

10.1214/aop/1176988861

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper we will consider translation invariant finite range particle systems with state space {0,1,..., kappa-1)S with S = epsilonZ(d). De Masi, Ferrari and Lebowitz have shown that if we introduce stirring at rate epsilon-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.

引用

页码：289 / 333

页数：45

共 23 条

[1]

[Anonymous], 1985, INTERACTING PARTICLE

[2]

Aronson D., 1975, PARTIAL DIFFERENTIAL, P5, DOI DOI 10.1007/BFB0070595

[3] MULTIDIMENSIONAL NON-LINEAR DIFFUSION ARISING IN POPULATION-GENETICS [J].