2004/06/30 by Yevgeniy Kovchegov, Kovchegov, Yevgeniy
Mathematics · #60K35 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60K35
paper · pdf · doi:10.48550/arxiv.math/0407005
23 pages
arxiv created 2004/11/09 · arxiv updated 2009/12/01
We introduce the mathematical theory of the particle systems that interact via permutations, where the transition rates are assigned not to the jumps from a site to a site, but to the permutations themselves. This permutation processes can be viewed as a generalization of the symmetric exclusion processes, where particles interact via transpositions. The duality and coupling techniques for the processes are described, the needed conditions for them to apply are established. The stationary distributions of the permutation processes are explored for translation invariant cases.