Equilibrium Kawasaki dynamics of continuous particle systems

Details Equilibrium Kawasaki dynamics of continuous particle systems Equilibrium Kawasaki dynamics of continuous particle systems

2005-03-02

arxiv.org/abs/math/0503042v2

Mathematics

Probability

Scientific paper

We construct a new equilibrium dynamics of infinite particle systems in a Riemannian manifold $X$. This dynamics is an analog of the Kawasaki dynamics of lattice spin systems. The Kawasaki dynamics now is a process where interacting particles randomly hop over $X$. We establish conditions on the {\it a priori} explicitly given symmetrizing measure and the generator of this dynamics, under which a corresponding conservative Markov processes exists. We also outline two types of scaling limit of the equilibrium Kawasaki dynamics: one leading to an equilibrium Glauber dynamics in continuum (a birth-and-death process), and the other leading to a diffusion dynamics of interacting particles (in particular, the gradient stochastic dynamics).

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