Non-equilibrium dynamics for a Widom-Rowlinson type model with mutations

Abstract

A dynamical version of the Widom-Rowlinsom model in the continuum is considered. The dynamics is modelled by a spatial two-component birth-and-death Glauber process where particles, in addition, are allowed to change their type with density dependent rates. An evolution of states is constructed as the unique weak solution to the associated Fokker-Planck equation. Such solution is obtained by means of its correlation functions which belong to a certain Ruelle space. Existence of a unique invariant measure and ergodicity with exponential rate is established. The mesoscopic limit is considered, it is related with the verification of the chaos preservation property.

References in corpus (4)

• Complete Analysis of Phase Transitions and Ensemble Equivalence for the Curie-Weiss-Potts Model
• Spatial birth and death processes as solutions of stochastic equations
• Dynamical Widom-Rowlinson model and its mesoscopic limit
• Evolution of states and mesoscopic scaling for two-component birth-and-death dynamics in continuum

Cited by in corpus (6)

• Linear evolution equations in scales of Banach spaces
• Stochastic averaging principle for spatial Markov evolutions in the continuum
• Evolution of states and mesoscopic scaling for two-component birth-and-death dynamics in continuum
• Stochastic averaging for a spatial population model in random environment
• Weak-coupling limit for ergodic environments
• Nonlinear perturbations of evolution systems in scales of Banach spaces