Duke Mathematical Journal

Amenability via random walks

Laurent Bartholdi and Bálint Virág

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Abstract

We use random walks to show that the Basilica group is amenable and thus answering an open question of Grigorchuk and Żuk [9]. Our results separate the class of amenable groups from the closure of subexponentially growing groups under the operations of group extension and direct limits; these classes are separated even within the realm of finitely presented groups.

Article information

Source
Duke Math. J., Volume 130, Number 1 (2005), 39-56.

Dates
First available in Project Euclid: 12 November 2005

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1131804019

Digital Object Identifier
doi:10.1215/S0012-7094-05-13012-5

Mathematical Reviews number (MathSciNet)
MR2176547

Zentralblatt MATH identifier
1104.43002

Subjects
Primary: 20E34: General structure theorems 60G50: Sums of independent random variables; random walks

Citation

Bartholdi, Laurent; Virág, Bálint. Amenability via random walks. Duke Math. J. 130 (2005), no. 1, 39--56. doi:10.1215/S0012-7094-05-13012-5. https://projecteuclid.org/euclid.dmj/1131804019


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