Random Walk on a Co-Compact Fuchsian Group
Probability
2012-05-20 v3 Group Theory
Abstract
It is proved that the Green's function of a symmetric finite range random walk on a co-compact Fuchsian group decays exponentially in distance at the radius of convergence R. It is also shown that Ancona's inequalities extend to R, and therefore that the Martin boundary for R-potentials coincides with the natural geometric boundary S^1, and that the Martin kernel is uniformly H\"older continuous. Finally, it is proved that this implies a local limit theorem for the transition probabilities.
Cite
@article{arxiv.1107.5591,
title = {Random Walk on a Co-Compact Fuchsian Group},
author = {Sébastien Gouëzel and Steven P. Lalley},
journal= {arXiv preprint arXiv:1107.5591},
year = {2012}
}
Comments
arXiv admin note: text overlap with arXiv:0710.5745