2007/09/14 by Eugene Lytvynov, E. Lytvynov, Lytvynov, E. +2
Mathematics · Physics and Astronomy · #60J75 #60J80 #60K35 #82C21 #82C22 #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60J75 #msc:60J80 #msc:60K35 #msc:82C21 #msc:82C22
paper · pdf · doi:10.48550/arxiv.0709.2284
arxiv created 2007/09/14 · openalex publication_date 2007/09/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We deal with two following classes of equilibrium stochastic dynamics of infinite particle systems in continuum: hopping particles (also called Kawasaki dynamics), i.e., a dynamics where each particle randomly hops over the space, and birth-and-death process in continuum (or Glauber dynamics), i.e., a dynamics where there is no motion of particles, but rather particles die, or are born at random. We prove that a wide class of Glauber dynamics can be derived as a scaling limit of Kawasaki dynamics. More precisely, we prove the convergence of respective generators on a set of cylinder functions, in the L2-norm with respect to the invariant measure of the processes. The latter measure is supposed to be a Gibbs measure corresponding to a potential of pair interaction, in the low activity-high temperature regime. Our result generalizes that of [Finkelshtein D.L. et al., to appear in Random Oper. Stochastic Equations], which was proved for a special Glauber (Kawasaki, respectively) dynamics.