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April, 1992 Equilibrium Behavior of the Sexual Reproduction Process with Rapid Diffusion
Chris Noble
Ann. Probab. 20(2): 724-745 (April, 1992). DOI: 10.1214/aop/1176989802


The sexual reproduction process is a reaction-diffusion type interacting particle system which exhibits phase transition. In this paper an upper bound is given for the critical value of the reaction rate and the equilibrium density is determined for all noncritical values of the reaction rate. The method of renormalized bond construction is the basis of our proof. Results for the hydrodynamic limit of the process are employed and some results for the associated nonlinear partial differential equation are developed to build the elements of this construction.


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Chris Noble. "Equilibrium Behavior of the Sexual Reproduction Process with Rapid Diffusion." Ann. Probab. 20 (2) 724 - 745, April, 1992.


Published: April, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0757.60104
MathSciNet: MR1159570
Digital Object Identifier: 10.1214/aop/1176989802

Primary: 60K35
Secondary: 35K57 , 60F99

Keywords: Equilibrium , Hydrodynamic limit , Interacting particle system , reaction-diffusion equation

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.20 • No. 2 • April, 1992
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