Markov Evolution of Continuum Particle Systems with Dispersion and Competition

2011/12/05 by Dmitri Finkelshtein, Yuri Kondratiev, Finkelshtein, Dmitri +5
Mathematics · Physics and Astronomy · #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math-ph #math.DS #math.MP #math.PR #msc:60J80 #msc:82C22 #msc:92D25

paper · pdf · doi:10.48550/arxiv.1112.0895

43 pages

arxiv created 2012/04/06 · arxiv updated 2012/04/09

Abstract

We construct birth-and-death Markov evolution of states(distributions) of point particle systems in ℝ^d. In this evolution, particles reproduce themselves at distant points (disperse) and die under the influence of each other (compete). The main result is a statement that the corresponding correlation functions evolve in a scale of Banach spaces and remain sub-Poissonian, and hence no clustering occurs, if the dispersion is subordinate to the competition.

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