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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. doi:10.4007/annals.2019.190.1.5.

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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 Paper
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).
Funding AgencyGrant Number
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:
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,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:97403
Deposited By: Tony Diaz
Deposited On:25 Jul 2019 16:20
Last Modified:16 Nov 2021 17:31

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