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Zapiski Nauchnykh Seminarov POMI, 2011, Volume 390, Pages 210–236
(Mi znsl4552)
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This article is cited in 6 scientific papers (total in 6 papers)
Quasimorphisms, random walks, and transient subsets in countable groups
A. V. Malyutin St. Petersburg Department Steklov Mathematical Institute RAN, St. Petersburg, Russia
Abstract:
We study interrelations between the theory of quasimorphisms and theory of random walks on groups, and establish the following criterion of transience for subsets of groups: if a subset of a countable group has bounded images under any three linearly independent homogeneous quasimorphisms on the group, then this subset is transient for all nondegenerate random walks on the group. From this it follows by results of M. Bestvina, K. Fujiwara, J. Birman, W. Menasco, and others that, in a certain sense, generic elements in mapping class groups of surfaces are pseudo-Anosov, generic braids in Artin's braid groups represent prime links and knots, generic elements in the commutant of every non-elementary hyperbolic group have large stable commutator length, etc.
Key words and phrases:
quasimorphism, random walk, transience, mapping class group, pseudo-Anosov, braid, knot, commutator.
Received: 15.02.2011
Citation:
A. V. Malyutin, “Quasimorphisms, random walks, and transient subsets in countable groups”, Representation theory, dynamical systems, combinatorial methods. Part XX, Zap. Nauchn. Sem. POMI, 390, POMI, St. Petersburg, 2011, 210–236; J. Math. Sci. (N. Y.), 181:6 (2012), 871–885
Linking options:
https://www.mathnet.ru/eng/znsl4552 https://www.mathnet.ru/eng/znsl/v390/p210
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Abstract page: | 572 | Full-text PDF : | 111 | References: | 47 |
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