2017/11/21 by Pierre Rousselin, Rousselin, Pierre
Mathematics · Physics and Astronomy · #37A50 (Primary) 60J05 #60J10 (Secondary) #60J50 #60J80 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · doi:10.48550/arxiv.1711.07920
openalex publication_date 2017/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the dimension drop phenomenon holds for the harmonic measure associated to a transient random walk in a random environment (as defined by R. Lyons and R. Pemantle in 1992 and generalized by G. Faraud in 2011) on an infinite Galton-Watson tree without leaves. We use regeneration times and ergodic theory techniques from the work of R. Lyons, R. Pemantle and Y. Peres in 1996 to give an explicit construction of the invariant measure for the forward environment seen by the particule at exit times which is absolutely continuous with respect to the joint law of the tree and the path of the random walk.