## Duke Mathematical Journal

### Piecewise automatic groups

Anna Erschler

#### Abstract

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 $f{:} {\mathbb N} \to {\mathbb N}$, there exists a finitely generated torsion group of intermediate growth $G$ for which the Følner function satisfies $\mathrm{Føl}_{G,S}{(n)\ge f(n)}$ 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

#### Article information

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

Dates
First available in Project Euclid: 28 August 2006

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1156771904

Digital Object Identifier
doi:10.1215/S0012-7094-06-13435-X

Mathematical Reviews number (MathSciNet)
MR2254627

Zentralblatt MATH identifier
1159.20019

#### Citation

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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