2022/09/05 by Georgii Veprev, Veprev, Georgii
Mathematics · Physics and Astronomy · #28D15 #28D20 #37A15 #37A35 #Dynamical Systems (math.DS) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2209.01902
openalex publication_date 2022/09/05 · openalex created_date 2022/09/30 · openalex updated_date 2026/08/01
We prove that a generic p.m.p. action of a countable amenable group G has scaling entropy that can not be dominated by a given rate of growth. As a corollary, we obtain that there does not exist a topological action of G for which the set of ergodic invariant measures coincides with the set of all ergodic p.m.p. G-systems of entropy zero. We also prove that a generic action of a residually finite amenable group has scaling entropy that can not be bounded from below by a given sequence. We also show an example of an amenable group that has such lower bound for every free p.m.p. action.