The Asymptotic Behavior of the Ergodic Measure of a Glauber + Kawasaki model
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We consider an interacting particle system given by the Glauber + Kawasaki dynamics. It is known that this process has a reaction diffusion equation as hydrodynamic limit. The ergodicity of this process in the presence of a metastable state (double well potential) was recently proved by S. Brassesco et al. In this Letter we prove that, in the limit, as ε → 0, the expected value of each spin converges to the global minimizer of the potential. We also prove decay of correlations of the ergodic measure.
Keywordsexit times interacting particle systems Glauber + Kawasaki dynamics reaction diffusion equations hydrodynamic limits
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