Context-free pairs of groups. II - cuts, tree sets, and random walks
Group Theory
2012-12-04 v1 Probability
Abstract
This is a continuation of the study, begun by Ceccherini-Silberstein and Woess, of context-free pairs of groups and the related context-free graphs in the sense of Muller and Schupp. Instead of the cones (connected components with respect to deletion of finite balls with respect to the graph metric), a more general approach to context-free graphs is proposed via tree sets consisting of cuts of the graph, and associated structure trees. The existence of tree sets with certain "good" properties is studied. With a tree set, a natural context-free grammar is associated. These investigations of the structure of context free pairs, resp. graphs are then applied to study random walk asymptotics via complex analysis.
Keywords
Cite
@article{arxiv.0911.0134,
title = {Context-free pairs of groups. II - cuts, tree sets, and random walks},
author = {Wolfgang Woess},
journal= {arXiv preprint arXiv:0911.0134},
year = {2012}
}