## M.: Equilibrium Kawasaki dynamics of continuous particle systems (2007)

Venue: | Infin. Dimens. Anal. Quantum Probab. Relat. Top |

Citations: | 3 - 2 self |

### BibTeX

@ARTICLE{Kondratiev07m.:equilibrium,

author = {Yuri Kondratiev and Eugene Lytvynov and Michael Röckner},

title = {M.: Equilibrium Kawasaki dynamics of continuous particle systems},

journal = {Infin. Dimens. Anal. Quantum Probab. Relat. Top},

year = {2007}

}

### OpenURL

### Abstract

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 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).