Mathematics – Probability
Scientific paper
2007-02-07
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 diffusive limit of such a dynamics, derived through a scaling of both the jump rate and time. Under weak assumptions on the potential of pair interaction, $\phi$, (in particular, admitting a singularity of $\phi$ at zero), we prove that, on a set of smooth local functions, the generator of the scaled dynamics converges to the generator of the gradient stochastic dynamics. If the set on which the generators converge is a core for the diffusion generator, the latter result implies the weak convergence of finite-dimensional distributions of the corresponding equilibrium processes. In particular, if the potential $\phi$ is from $C_{\mathrm b}^3(\mathbb R^d)$ and sufficiently quickly converges to zero at infinity, we conclude the convergence of the processes from a result in [Choi {\it et al.}, J. Math. Phys. 39 (1998) 6509--6536].
Kondratiev Yuri G.
Kutoviy Oleksandr V.
Lytvynov Eugene W.
No associations
LandOfFree
Diffusion approximation for equilibrium Kawasaki dynamics in continuum 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 Diffusion approximation for equilibrium Kawasaki dynamics in continuum, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Diffusion approximation for equilibrium Kawasaki dynamics in continuum will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-218957