Asymptotic entropy and Green speed for random walks on countable groups

By S'ebastien Blachere, Peter Haissinsky, Pierre Mathieu. 2006

56 citations recorded by the source corpus.

We study asymptotic properties of the Green metric associated with transient random walks on countable groups. We prove that the rate of escape of the random walk computed in the Green metric equals its asymptotic entropy. The proof relies on integral representations of both quantities with the extended Martin kernel. In the case of finitely generated groups, where this result is known (Benjamini and Peres [Probab. Theory Related Fields 98 (1994) 91–112]), we give an alternative proof relying on a version of the so-called fundamental inequality (relating the rate of escape, the entropy and the logarithmic volume growth) extended to random walks with unbounded support.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f2549d4dc3a63967c1ff26cbc542cbe729b89f07

Citations in the corpus

• Random walks on co-compact fuchsian groups (2013, unknown): “The Green metric associated with F1 has been used by a number of authors, for instance in [7], [8] and [9].”
• Harmonic measures versus quasiconformal measures for hyperbolic groups (2008, unknown): “On the other hand,”