A zero-one law for recurrence and transience of frog processes

2015/08/08 by Elena Kosygina, Kosygina, Elena, Martin Zerner +2
Mathematics · #60J10 #60K35 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR #msc:60J10 #msc:60K35

paper · pdf · doi:10.48550/arxiv.1508.01953

30 pages; revised version

openalex publication_date 2015/08/08 · arxiv created 2016/02/21 · arxiv updated 2016/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide sufficient conditions for the validity of a dichotomy, i.e. zero-one law, between recurrence and transience of general frog models. In particular, the results cover frog models with i.i.d. numbers of frogs per site where the frog dynamics are given by quasi-transitive Markov chains or by random walks in a common random environment including super-critical percolation clusters on ℤ^d. We also give a sufficient and almost sharp condition for recurrence of uniformly elliptic frog processes on ℤ^d. Its proof uses the general zero-one law.

Citations

• The speed of frogs with drift on ℤ

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