English

Regular sets and counting in free groups

Group Theory 2009-06-17 v1 Probability

Abstract

In this paper we study asymptotic behavior of regular subsets in a free group F of finite rank, compare their sizes at infinity, and develop techniques to compute the probabilities of sets relative to distributions on F that come naturally from no-return random walks on the Cayley graph of F. We apply these techniques to study cosets, double cosets, and Schreier representatives of finitely generated subgroups of F and also to analyze relative sizes of regular prefixed-closed subsets in F.

Keywords

Cite

@article{arxiv.0906.2850,
  title  = {Regular sets and counting in free groups},
  author = {Elizaveta Frenkel and Alexei G. Myasnikov and Vladimir N. Remeslennikov},
  journal= {arXiv preprint arXiv:0906.2850},
  year   = {2009}
}

Comments

33 pp, 5 figures