2016/04/26 by Joanna Barańska, Yuri Kozitsky, Baranska, Joanna +1
Mathematics · Physics and Astronomy · #60K35 #70F45 #82C22 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1604.07735
openalex publication_date 2016/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the dynamics of an infinite system of point particles of two types. They perform random jumps in Rd in the course of which particles of different types repel each other whereas those of the same type do not interact. The states of the system are probability measures on the corresponding configuration space, the global (in time) evolution of which is constructed by means of correlation functions. It is proved that for each initial sub-Poissonian state μ0, the states evolve μ0 ↦ μt in such a way that μt is sub-Poissonian for all t>0. The mesoscopic (approximate) description of the evolution of states is also given. The stability of translation invariant stationary states is studied. In particular, we show that some of such states can be unstable with respect to space-dependent perturbations.