Abstract:
The paper analyses the entropy and the normalised drift of wreath product of finitely generated groups. Examples of groups of zero entropy are given.
Citation:
A. Dubina, “Characteristics of random walks on wreath products”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part III, Zap. Nauchn. Sem. POMI, 256, POMI, St. Petersburg, 1999, 31–37; J. Math. Sci. (New York), 107:5 (2001), 4166–4171
\Bibitem{Dyu99}
\by A.~Dubina
\paper Characteristics of random walks on wreath products
\inbook Representation theory, dynamical systems, combinatorial and algoritmic methods. Part~III
\serial Zap. Nauchn. Sem. POMI
\yr 1999
\vol 256
\pages 31--37
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl969}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1708557}
\zmath{https://zbmath.org/?q=an:0984.60020}
\transl
\jour J. Math. Sci. (New York)
\yr 2001
\vol 107
\issue 5
\pages 4166--4171
\crossref{https://doi.org/10.1023/A:1012465406149}
Linking options:
https://www.mathnet.ru/eng/znsl969
https://www.mathnet.ru/eng/znsl/v256/p31
This publication is cited in the following 9 articles:
Bartholdi L., Erschler A., “Poisson-Furstenberg Boundary and Growth of Groups”, Probab. Theory Relat. Field, 168:1-2 (2017), 347–372
L. A. Gilch, “Rate of escape on the lamplighter tree”, J Math Sci, 156:1 (2009), 173
Gilch L.A., “Rate of escape of random walks on free products”, Journal of the Australian Mathematical Society, 83:1 (2007), 31–54
Erschler A., “Isoperimetry for wreath products of Markov chains and multiplicity of selfintersections of random walks”, Probab Theory Related Fields, 136:4 (2006), 560–586
Erschler A., “Boundary behavior for groups of subexponential growth”, Ann of Math (2), 160:3 (2004), 1183–1210
Erschler A., “Liouville property for groups and manifolds”, Invent Math, 155:1 (2004), 55–80
Erschler A., “On isoperimetric profiles of finitely generated groups”, Geom Dedicata, 100:1 (2003), 157–171
Erschler A., “On drift and entropy growth for random walks on groups”, Ann Probab, 31:3 (2003), 1193–1204
Steven Evans, “Eigenvalues of Random Wreath Products”, Electron. J. Probab., 7:none (2002)