2009/11/02 by Andrea Collevecchio, Collevecchio, Andrea, Tom Schmitz +1
Decision Sciences · Mathematics · #60K37 #60K99 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics #math.PR #msc:60K37 #msc:60K99
paper · pdf · doi:10.48550/arxiv.0911.0305
21 pages
arxiv created 2009/11/02 · openalex publication_date 2009/11/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop a technique that provides a lower bound on the speed of transient random walk in a random environment on regular trees. A refinement of this technique yields upper bounds on the first regeneration level and regeneration time. In particular, a lower and upper bound on the covariance in the annealed invariance principle follows. We emphasize the fact that our methods are general and also apply in the case of once-reinforced random walk. Durrett, Kesten and Limic (2002) prove an upper bound of the form b/(b+δ) for the speed on the b-ary tree, where δ is the reinforcement parameter. For δ>1 we provide a lower bound of the form γ2 b/(b+δ), where γ is the survival probability of an associated branching process.