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Choquet-Deny groups and the infinite conjugacy class property

Frisch, Joshua and Hartman, Yair and Tamuz, Omer and Vahidi Ferdowsi, Pooya (2019) Choquet-Deny groups and the infinite conjugacy class property. Annals of Mathematics, 190 (1). pp. 307-320. ISSN 0003-486X. https://resolver.caltech.edu/CaltechAUTHORS:20190725-090144871

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Abstract

A countable discrete group G is called Choquet-Deny if for every non-degenerate probability measure μ on G, it holds that all bounded μ-harmonic functions are constant. We show that a finitely generated group G is Choquet-Deny if and only if it is virtually nilpotent. For general countable discrete groups, we show that G is Choquet-Deny if and only if none of its quotients has the infinite conjugacy class property. Moreover, when G is not Choquet-Deny, then this is witnessed by a symmetric, finite entropy, non-degenerate measure.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.4007/annals.2019.190.1.5DOIArticle
https://arxiv.org/abs/1802.00751arXivDiscussion Paper
ORCID:
AuthorORCID
Tamuz, Omer0000-0002-0111-0418
Additional Information:© 2019 Department of Mathematics, Princeton University. J. Frisch was supported by NSF Grant DMS-1464475. Y. Hartman was partially supported by the Israel Science Foundation (grant No. 1175/18). He is grateful for the support of Northwestern University, where he was a postdoctoral fellow when most of this research was conducted. O. Tamuz was supported by a grant from the Simons Foundation (#419427).
Funders:
Funding AgencyGrant Number
NSFDMS-1464475
Israel Science Foundation1175/18
Northwestern UniversityUNSPECIFIED
Simons Foundation419427
Subject Keywords:Furstenberg-Poisson boundary, random walks, harmonic functions
Issue or Number:1
Classification Code:AMS Classification: Primary: 60B15
Record Number:CaltechAUTHORS:20190725-090144871
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190725-090144871
Official Citation:Frisch, Joshua, et al. “Choquet-Deny Groups and the Infinite Conjugacy Class Property.” Annals of Mathematics, vol. 190, no. 1, 2019, pp. 307–320. JSTOR, www.jstor.org/stable/10.4007/annals.2019.190.1.5
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:97403
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:25 Jul 2019 16:20
Last Modified:03 Oct 2019 21:31

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