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- W2114119128 abstract "We study the problem of identication of a proper state-space for the stochastic dynamics of free particles in continuum, with their possible birth and death. In this dynamics, the motion of each separate particle is described by a x ed Markov process M on a Riemannian manifold X. The main problem arising here is a possible collapse of the system, in the sense that, though the initial congur ation of particles is locally nite , there could exist a compact set in X such that, with probability one, innitely many particles will arrive at this set at some time t > 0. We assume that X has innite volume and, for each > 1, we consider the set of all innite congur ations in X for which the number of particles in a compact set is bounded by a constant times the -th power of the volume of the set. We nd quite general conditions on the process M which guarantee that the corresponding innite particle process can start at each congur ation from , will never leave , and has cadlag (or, even, continuous) sample paths in the vague topology. We consider the following examples of applications of our results: Brownian motion on the congur ation space, free Glauber dynamics on the congur ation space (or a birth-and-death process in X), and free Kawasaki dynamics on the congur ation space. We also show that if X = R d , then for a wide class of starting distributions, the (non-equilibrium) free Glauber dynamics is a scaling limit of (non-equilibrium) free Kawasaki dynamics." @default.
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- W2114119128 date "2007-01-25" @default.
- W2114119128 modified "2023-09-27" @default.
- W2114119128 title "Non-equilibrium stochastic dynamics in continuum: The free case" @default.
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