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January, 1994 Spatial Patterns when Phases Separate in an Interacting Particle System
A. De Masi, A. Pellegrinotti, E. Presutti, M. E. Vares
Ann. Probab. 22(1): 334-371 (January, 1994). DOI: 10.1214/aop/1176988862


We consider a one-dimensional Glauber-Kawasaki process which gives rise in the hydrodynamical limit to a reaction diffusion equation with a double-well potential. We study the case when the process starts off from a product measure with zero averages, which, hydrodynamically, corresponds to a stationary unstable state. We prove that at times longer than the hydrodynamical ones the reaction diffusion equation no longer describes the behavior of the system, which in fact leaves the unstable equilibrium. The spatial patterns of the typical configurations when this happens are investigated.


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A. De Masi. A. Pellegrinotti. E. Presutti. M. E. Vares. "Spatial Patterns when Phases Separate in an Interacting Particle System." Ann. Probab. 22 (1) 334 - 371, January, 1994.


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

zbMATH: 0830.60092
MathSciNet: MR1258880
Digital Object Identifier: 10.1214/aop/1176988862

Primary: 60K35
Secondary: 60F05 , 82A05

Keywords: interacting particle systems , reaction diffusion equation , unstable equilibria

Rights: Copyright © 1994 Institute of Mathematical Statistics


Vol.22 • No. 1 • January, 1994
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