2021/12/22 by George Andriopoulos, Andriopoulos, George, Eleanor Archer +1
Mathematics · Physics and Astronomy · #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.2112.12037
openalex publication_date 2021/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove an invariance principle for linearly edge reinforced random walks on γ-stable critical Galton-Watson trees, where γ∈ (1,2] and where the edge joining x to its parent has rescaled initial weight d(ρ, x)α for some α≤ 1. This corresponds to the recurrent regime of initial weights. We then establish fine asymptotics for the limit process. In the transient regime, we also give an upper bound on the random walk displacement in the discrete setting, showing that the edge reinforced random walk never has positive speed, even when the initial edge weights are strongly biased away from the root.