Equilibrium Kawasaki dynamics of continuous particle systems

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