2024/10/11 by Tabea Glatzel, Glatzel, Tabea, Jan Nagel +1
Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2410.08768
We show a central limit theorem for random walk on a Galton-Watson tree, when the edges of the tree are assigned randomly uniformly elliptic conductances. When a positive fraction of edges is assigned a small conductance ε, we study the behavior of the limiting variance as ε→ 0. Provided that the tree formed by larger conductances is supercritical, the variance is nonvanishing as ε→ 0, which implies that the slowdown induced by the ε-edges is not too strong. The proof utilizes a specific regeneration structure, which leads to escape estimates uniform in ε.