Equilibrium Glauber dynamics of continuous particle systems as a scaling limit of Kawasaki dynamics
| dc.creator | Finkelshtein, Dmitri L. | |
| dc.creator | Kondratiev, Yuri G. | |
| dc.creator | Lytvynov, Eugene W. | |
| dc.date | 2006-08-02 | |
| dc.date.accessioned | 2026-07-07T07:21:17Z | |
| dc.date.available | 2026-07-07T07:21:17Z | |
| dc.description | A Kawasaki dynamics in continuum is a dynamics of an infinite system of interacting particles in $\mathbb{R}^d$ which randomly hop over the space. In this paper, we deal with an equilibrium Kawasaki dynamics which has a Gibbs measure $mu$ as invariant measure. We study a scaling limit of such a dynamics, derived through a scaling of the jump rate. Informally, we expect that, in the limit, only jumps of ``infinite length'' will survive, i.e., we expect to arrive at a Glauber dynamics in continuum (a birth-and-death process in $\mathbb{R}^d$). We prove that, in the low activity-high temperature regime, the generators of the Kawasaki dynamics converge to the generator of a Glauber dynamics. The convergence is on the set of exponential functions, in the $L^2(μ)$-norm. Furthermore, additionally assuming that the potential of pair interaction is positive, we prove the weak convergence of the finite-dimensional distributions of the processes. | |
| dc.identifier | https://arxiv.org/abs/math/0608051 | |
| dc.identifier | http://arxiv.org/abs/math/0608051 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115251 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | 60K35, 60J75, 60J80, 82C21, 82C22 | |
| dc.title | Equilibrium Glauber dynamics of continuous particle systems as a scaling limit of Kawasaki dynamics | |
| dc.type | text |