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**1 - 1**of**1**### Binary jumps in continuum. II. Non-equilibrium process and a Vlasov-type scaling limit

, 2011

"... Let Γ denote the space of all locally finite subsets (configurations) in Rd. A stochastic dynamics of binary jumps in continuum is a Markov process on Γ in which pairs of particles simultaneously hop over Rd. We discuss a non-equilibrium dynamics of binary jumps. We prove the exis-tence of an evolut ..."

Abstract
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Let Γ denote the space of all locally finite subsets (configurations) in Rd. A stochastic dynamics of binary jumps in continuum is a Markov process on Γ in which pairs of particles simultaneously hop over Rd. We discuss a non-equilibrium dynamics of binary jumps. We prove the exis-tence 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. Key words: continuous system, binary jumps, non-equilibrium dynamics, correlation