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 , there exists a finitely generated torsion group of intermediate growth for which the Følner function satisfies for some generating set and all sufficiently large . 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
Citation
Anna Erschler. "Piecewise automatic groups." Duke Math. J. 134 (3) 591 - 613, 15 September 2006. https://doi.org/10.1215/S0012-7094-06-13435-X
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