Ergodic theory on Galton—Watson trees: speed of random walk and dimension of harmonic measure

  title={Ergodic theory on Galton—Watson trees: speed of random walk and dimension of harmonic measure},
  author={Russell Lyons and Robin Pemantle and Yuval Peres},
  journal={Ergodic Theory and Dynamical Systems},
  pages={593 - 619}
Abstract We consider simple random walk on the family tree T of a nondegenerate supercritical Galton—Watson branching process and show that the resulting harmonic measure has a.s. strictly smaller Hausdorff dimension than that of the whole boundary of T. Concretely, this implies that an exponentially small fraction of the nth level of T carries most of the harmonic measure. First-order asymptotics for the rate of escape, Green function and the Avez entropy of the random walk are also determined… 
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