2023/11/29 by Georgii Veprev, Veprev, Georgii
Mathematics · Biochemistry, Genetics and Molecular Biology · #Mathematical Dynamics and Fractals #Geometric and Algebraic Topology #Protein Structure and Dynamics
paper · pdf · doi:10.48550/arxiv.2311.17580
The scaling entropy of a p.m.p. action is a slow-entropy type invariant that characterizes the intermediate growth of entropy in a dynamical system. An amenable group G has a scaling entropy growth gap if the scaling entropy of any its free p.m.p. action admits a non-trivial lower bound. We prove that the group S_∞ of all finite permutations has a scaling entropy growth gap as well as the Houghton group H2. By proving this, we show that there are finitely generated amenable groups with this property.