Vershik, A. M. Numerical characteristics of groups and the relations between them. (English. Russian original) Zbl 0996.20057 J. Math. Sci., New York 107, No. 5, 4147-4157 (2001); translation from Zap. Nauchn. Semin. POMI 256, 5-18 (1999). Summary: The entropy of a random walk on a discrete countable group can be used for comparison of systems of generators. A fundamental inequality between growth, entropy and escape rate gives the possibility to define “the best” system of generators. We formulate a new circle of problems related to growth and other asymptotic characteristics of groups. Cited in 3 ReviewsCited in 1 Document MSC: 20P05 Probabilistic methods in group theory 20F05 Generators, relations, and presentations of groups 60G50 Sums of independent random variables; random walks 20F69 Asymptotic properties of groups 28D20 Entropy and other invariants 60B15 Probability measures on groups or semigroups, Fourier transforms, factorization Keywords:entropy; random walks; systems of generators; growth conditions; asymptotic properties PDFBibTeX XMLCite \textit{A. M. Vershik}, J. Math. Sci., New York 107, No. 5, 4147--4157 (1999; Zbl 0996.20057); translation from Zap. Nauchn. Semin. POMI 256, 5--18 (1999) Full Text: DOI