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.
Duke Math. J.
130(1):
39-56
(01 October 2005).
DOI: 10.1215/S0012-7094-05-13012-5
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