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P.T.: On convergence of generators of equilibrium dynamics of hopping particles to generator of a birth-and-death process in continuum. To appear
| Venue: | In: Proceedings of the International Conference on Infinite Particle Systems, 8–11 October 2006, Kazimierz Dolny |
| Citations: | 1 - 1 self |
BibTeX
@INPROCEEDINGS{Lytvynov_p.t.:on,
author = {E Lytvynov and P T Polara},
title = {P.T.: On convergence of generators of equilibrium dynamics of hopping particles to generator of a birth-and-death process in continuum. To appear},
booktitle = {In: Proceedings of the International Conference on Infinite Particle Systems, 8–11 October 2006, Kazimierz Dolny},
year = {}
}
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Abstract
We deal with the two following classes of equilibrium stochastic dynamics of infinite particle systems in continuum: hopping particles (also called Kawasaki dynamics), i.e., a dynamics where each particle randomly hops over the space, and birth-and-death process in continuum (or Glauber dynamics), i.e., a dynamics where there is no motion of particles, but rather particles die, or are born at random. We prove that a wide class of Glauber dynamics can be derived as a scaling limit of Kawasaki dynamics. More precisely, we prove the convergence of respective generators on a set of cylinder functions, in the L 2 -norm with respect to the invariant measure of the processes. The latter measure is supposed to be a Gibbs measure corresponding to a potential of pair interaction, in the low activity-high temperature regime. Our result generalizes that of [Random. Oper. Stoch. Equa., 2007, 15, 105], which was proved for a special Glauber (Kawasaki, respectively) dynamics.
