A Case Leading to Rationality of the Drift
Let G be an infinite finitely generated group endowed with a measure of probability and a left-invariant metric. Let ∂ G be the horofunction compactification. Using a representation of the drift via horofunctions, we establish one situation in which we have rationality of the drift.
KeywordsProbability Measure Random Walk Compact Group Uniform Convergence Rational Coefficient
- 2.Karlsson, A.: Ergodic theorems for noncommutting random products, Lectures notes from Santiago and Wroclaw, unpublished (2008)Google Scholar
- 3.Karlsson, A., Ledrappier, F.: Linear drift and Poisson boundary for random walks. Pure Appl. Math. Q., Pt 1 3(4), 1027–1036 (2007)Google Scholar
- 4.Karlsson, A., Ledrappier, F.: Noncommutative ergodic theorems. In: Farb, B., Fisher, D. (eds.) Geometry, Rigidity, and Group Actions. Chicago Lectures in Mathematics Series, vol. 75. The University of Chicago Press, Chicago (2011)Google Scholar