2002/04/05 by Alexandre V. Borovik, Alexandre Borovik, Alexei G. Myasnikov +6
Computer Science · Mathematics · #20E05 #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Probability (math.PR) #math.GR #math.PR #msc:20E05 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.math/0204070
LaTeX, requires amssymb.sty; 31 pp Version 3: more detail in Example 2 and Tauberian theorems
openalex publication_date 2002/04/05 · arxiv created 2002/04/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a family of atomic measures on free groups generated by no-return random walks. These measures are shown to be very convenient for comparing "relative sizes" of subgroups, context-free and regular subsets (that, subsets generated by finite automata) of free groups. Many asymptotic characteristics of subsets and subgroups are naturally expressed as analytic properties of related generating functions. We introduce an hierarchy of asymptotic behaviour "at infinity" of subsets in the free groups, more sensitive than the traditionally used asymptotic density, and apply it to normal subgroups and regular subsets.