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

Abstract

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.

References in corpus (4)

• Vlasov scaling for stochastic dynamics of continuous systems
• Operator approach to Vlasov scaling for some models of spatial ecology
• Binary jumps in continuum. I. Equilibrium processes and their scaling limits
• A note on equilibrium Glauber and Kawasaki dynamics for fermion point processes

Cited by in corpus (2)

• Binary jumps in continuum. I. Equilibrium processes and their scaling limits
• Asymptotic Behavior of the Subordinated Traveling Waves