Predictability, topological entropy, and invariant random orders

Andrei Alpeev, Tom Meyerovitch, Sieye Ryu

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We prove that a topologically predictable action of a countable amenable group has zero topological entropy, as conjectured by Hochman. We investigate invariant random orders and formulate a unified Kieffer-Pinsker formula for the Kolmogorov-Sinai entropy of measure preserving actions of amenable groups. We also present a proof due to Weiss for the fact that topologically prime actions of sofic groups have non-positive topological sofic entropy.

Original languageEnglish
Pages (from-to)1443-1457
Number of pages15
JournalProceedings of the American Mathematical Society
Volume149
Issue number4
DOIs
StatePublished - 1 Apr 2021

Keywords

  • Amenable groups
  • Random invaraint orders
  • Sofic groups
  • Topological entropy
  • Topological predictability

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics

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