Binary jumps in continuum. II. Non-equilibrium process and a Vlasov-type scaling limit

Details Binary jumps in continuum. II. Non-equilibrium process and a Vlasov-type scaling limit Binary jumps in continuum. II. Non-equilibrium process and a Vlasov-type scaling limit

2011-07-20

arxiv.org/abs/1107.4005v1

Mathematics

Probability

Scientific paper

Let $\Gamma$ denote the space of all locally finite subsets (configurations) in $\mathbb R^d$. A stochastic dynamics of binary jumps in continuum is a Markov process on $\Gamma$ in which pairs of particles simultaneously hop over $\mathbb R^d$. We discuss a non-equilibrium dynamics of binary jumps. We prove the existence of an evolution of correlation functions on a finite time interval. We also show that a Vlasov-type mesoscopic scaling for such a dynamics leads to a generalized Boltzmann non-linear equation for the particle density.

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