@article{44246bae4f004a8bb186f3f15078a353,
title = "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. 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.",
keywords = "Amenable groups, Random invaraint orders, Sofic groups, Topological entropy, Topological predictability",
author = "Andrei Alpeev and Tom Meyerovitch and Sieye Ryu",
note = "Funding Information: Received by the editors February 5, 2019, and, in revised form, July 15, 2019. 2010 Mathematics Subject Classification. Primary 37B40, 37A35. Key words and phrases. Topological entropy, random invaraint orders, topological predictability, amenable groups, sofic groups. The first author was supported by “Native towns”, a social investment program of PJSC “Gazprom Neft”. The second and third authors acknowledge support by the Israel Science Foundation (grants no. 626/14 and 1052/18) and the The Center For Advanced Studies In Mathematics in Ben Gurion University. Publisher Copyright: {\textcopyright} 2021 American Mathematical Society.",
year = "2021",
month = apr,
day = "1",
doi = "https://doi.org/10.1090/proc/15158",
language = "American English",
volume = "149",
pages = "1443--1457",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "4",
}