On the speed of distance stationary sequences
Abstract
We prove a formula for the speed of distance stationary random sequences generalizing the law of large numbers of Karlsson and Ledrappier. A particular case is the classical formula for the largest Lyapunov exponent of i.i.d.\ matrix products, but our result has applications in various different contexts. In many situations it gives a method to estimate the speed, and in others it allows to obtain results of dimension drop for escape measures related to random walks. We show applications to stationary reversible random trees with conductances, Bernoulli bond percolation of Cayley graphs, and random walks on cocompact Fuchsian groups.
Keywords
Cite
@article{arxiv.1912.12523,
title = {On the speed of distance stationary sequences},
author = {Matias Carrasco and Pablo Lessa and Elliot Paquette},
journal= {arXiv preprint arXiv:1912.12523},
year = {2020}
}
Comments
This article overlaps the (almost twice as long) preprint arXiv:1710.00733 which will remain unpublished. Compared with said preprint the results on hyperbolic Poisson-Delaunay random walks have been removed, the exposition of the abstract formula for speed has been improved, and new applications of it are given