Diffusion approximation for equilibrium Kawasaki dynamics in continuum

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dc.creatorKondratiev, Y. G.
dc.creatorKutoviy, O. V.
dc.creatorLytvynov, E. W.
dc.date2007-02-07
dc.date2007-08-20
dc.date.accessioned2026-07-07T08:24:11Z
dc.date.available2026-07-07T08:24:11Z
dc.descriptionA 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 $μ$ 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, $ϕ$, (in particular, admitting a singularity of $ϕ$ 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 $ϕ$ 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].
dc.identifierhttps://arxiv.org/abs/math/0702178
dc.identifierhttp://arxiv.org/abs/math/0702178
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/136256
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject60F99, 60J60, 60J75, 60K35
dc.titleDiffusion approximation for equilibrium Kawasaki dynamics in continuum
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