Predictability, topological entropy, and invariant random orders

Andrei Alpeev; Tom Meyerovitch; Sieye Ryu

doi:10.1090/proc/15158

Predictability, topological entropy, and invariant random orders

Andrei Alpeev, Tom Meyerovitch, Sieye Ryu

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

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 language	American English
Pages (from-to)	1443-1457
Number of pages	15
Journal	Proceedings of the American Mathematical Society
Volume	149
Issue number	4
DOIs	https://doi.org/10.1090/proc/15158
State	Published - 1 Apr 2021

Keywords

Amenable groups
Random invaraint orders
Sofic groups
Topological entropy
Topological predictability

All Science Journal Classification (ASJC) codes

Applied Mathematics
General Mathematics

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10.1090/proc/15158

Cite this

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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.",

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AU - Ryu, Sieye

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N2 - 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.

AB - 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.

KW - Amenable groups

KW - Random invaraint orders

KW - Sofic groups

KW - Topological entropy

KW - Topological predictability

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JF - Proceedings of the American Mathematical Society

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ER -

Predictability, topological entropy, and invariant random orders

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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