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:N→N, there exists a finitely generated torsion group of intermediate growth G for which the Folner function satisfies FolG,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
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
