2009/06/16 by Frenkel, Elizaveta, Myasnikov, Alexei G., Remeslennikov, Vladimir N.
#20E05 #FOS: Mathematics #Group Theory (math.GR) #Probability (math.PR)
paper · doi:10.48550/arxiv.0906.2850
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.