Equilibrium Behavior of the Sexual Reproduction Process with Rapid Diffusion

Abstract

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.