2007/12/18 by Marcus Warfheimer, Warfheimer, Marcus
Mathematics · Physics and Astronomy · #60K35 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60K35
paper · pdf · doi:10.48550/arxiv.0712.2929
14 pages
openalex publication_date 2007/12/18 · arxiv created 2010/04/17 · arxiv updated 2010/04/20 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
We consider spin systems on \Z (i.e. interacting particle systems on \Z in which each coordinate only has two possible values and only one coordinate changes in each transition) whose rates are determined by another process, called a background process. A canonical example is the so called contact process in randomly evolving environment (CPREE), introduced and analysed by E. Broman and furthermore studied by J. Steif and the author, where the marginals of the background process independently evolve as 2-state Markov chains and determine the recovery rates for a contact process. We prove that under certain conditions on the rates there are at most two extremal stationary distributions. The proof follows closely the ideas of Liggett's proof of a corresponding theorem for spin systems on \Z without a background process.