Vershik, A. M.; Nechaev, S.; Bikbov, R. Statistical properties of locally free groups with applications to braid groups and growth of random heaps. (English) Zbl 1010.20056 Commun. Math. Phys. 212, No. 2, 469-501 (2000). Summary: The main statistical characteristics of locally free groups: the growth, the drift and the entropy are considered and relations between them are established. Our results assert that: (i) the statistical properties of random walks (Markov chains) on locally free and braid groups are not the same as the uniform statistics on these groups, and (ii) the stabilization of the statistical characteristics exists when the number of generators of the group grows. Cited in 19 Documents MSC: 20P05 Probabilistic methods in group theory 20F36 Braid groups; Artin groups 60B15 Probability measures on groups or semigroups, Fourier transforms, factorization Keywords:locally free groups; growth of groups; random walks; braid groups; numbers of generators PDFBibTeX XMLCite \textit{A. M. Vershik} et al., Commun. Math. Phys. 212, No. 2, 469--501 (2000; Zbl 1010.20056) Full Text: DOI