Duke Mathematical Journal

Piecewise automatic groups

Anna Erschler

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We introduce a notion of a piecewise automatic group. Among these groups we describe a new class of groups of intermediate growth. We show that for any function f:NN, there exists a finitely generated torsion group of intermediate growth G for which the Følner function satisfies FølG,S(n)f(n) for some generating set S and all sufficiently large n. As a corollary we see that the asymptotic entropy of simple random walks on these groups could be arbitrarily close to being linear, while the Poisson boundary is trivial

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Duke Math. J., Volume 134, Number 3 (2006), 591-613.

First available in Project Euclid: 28 August 2006

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Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 20F69: Asymptotic properties of groups 20E08: Groups acting on trees [See also 20F65] 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization
Secondary: 20F05: Generators, relations, and presentations 20F50: Periodic groups; locally finite groups


Erschler, Anna. Piecewise automatic groups. Duke Math. J. 134 (2006), no. 3, 591--613. doi:10.1215/S0012-7094-06-13435-X. https://projecteuclid.org/euclid.dmj/1156771904

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