Limit theorems for the empirical distribution of supercritical branching random walks on transitive graphs

Abstract

We consider supercritical branching random walks on transitive graphs and we prove a law of large numbers for the mean displacement of the ensemble of particles, and a Stam-type central limit theorem for the empirical distributions, thus answering the questions from Kaimanovich-Woess [KW23, Section 6.2].

Electronic Journal of Probability (2026); to appear