Mathematics – Probability
Scientific paper
2006-08-02
Mathematics
Probability
Scientific paper
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 $L^2(\mu)$-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.
Finkelshtein Dmitri L.
Kondratiev Yuri G.
Lytvynov Eugene W.
No associations
LandOfFree
Equilibrium Glauber dynamics of continuous particle systems as a scaling limit of Kawasaki dynamics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Equilibrium Glauber dynamics of continuous particle systems as a scaling limit of Kawasaki dynamics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Equilibrium Glauber dynamics of continuous particle systems as a scaling limit of Kawasaki dynamics will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-265064