Improved critical drift estimates for the frog model on trees

2023/09/25 by Poly Mathews, Mathews, Poly · 1 citation
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

paper · pdf · doi:10.48550/arxiv.2309.14443

openalex publication_date 2023/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Place an active particle at the root of the infinite d-ary tree and dormant particles at each non-root site. Active particles move towards the root with probability p and otherwise move to a uniformly sampled child vertex. When an active particle moves to a site containing dormant particles, all the particles at the site become active. The critical drift p_d is the infimum over all p for which infinitely many particles visit the root almost surely. We give improved bounds on sup_{d ≥ m} p_d and prove monotonicity of critical values associated to a self-similar variant.

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