2015/02/09 by Arka P. Ghosh, Arka Ghosh, Steven Noren +4
Computer Science · Mathematics · #33D05 #60K35 #Cellular Automata and Applications #FOS: Mathematics #Primary: 60J10 #Probability (math.PR) #Random Matrices and Applications #Secondary: 60E05 #Stochastic processes and statistical mechanics #math.PR #msc:33D05 #msc:60E05 #msc:60J10 #msc:60K35
paper · pdf · doi:10.48550/arxiv.1502.02738
arxiv created 2015/02/09 · openalex publication_date 2015/02/09 · arxiv updated 2015/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we observe the frog model, an infinite system of interacting random walks, on Z with an asymmetric underlying random walk. Under the assumption of transience with a fixed frog distribution, we construct an explicit formula for the moments of the lower bound of the model's long-run range, as well as their asymptotic limits as the drift of the underlying random walk vanishes. We also provide conditions in which the lower bound can be scaled to converge in probability to the degenerate distribution at 1 as the drift vanishes.