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

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

4 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 language	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

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.1090/proc/15158

Cite this

@article{7f66c1fb55a54bcb86a90e44bd45bbe4,

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 = "Publisher Copyright: {\textcopyright} 2021 American Mathematical Society.",

year = "2021",

month = apr,

day = "1",

doi = "10.1090/proc/15158",

language = "English",

volume = "149",

pages = "1443--1457",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "4",

}

TY - JOUR

T1 - Predictability, topological entropy, and invariant random orders

AU - Alpeev, Andrei

AU - Meyerovitch, Tom

AU - Ryu, Sieye

PY - 2021/4/1

Y1 - 2021/4/1

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

UR - http://www.scopus.com/inward/record.url?scp=85104592776&partnerID=8YFLogxK

U2 - 10.1090/proc/15158

DO - 10.1090/proc/15158

M3 - Article

AN - SCOPUS:85104592776

SN - 0002-9939

VL - 149

SP - 1443

EP - 1457

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 4

ER -

Predictability, topological entropy, and invariant random orders

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this