Predictability, topological entropy and invariant random orders

Abstract

We prove that a topologically predictable action of a countable amenable group has zero topological entropy, as conjectured by Hochman. On route, 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.

15 pages. Added reference to Ben Hayes's papers regarding "relative sofic entropy" of finite-to-one or compact extensions and regarding the "Abramov-Rokhlin sub-addition formula for sofic entropy"