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- W2045706494 abstract "The structure of a self-similar group G naturally gives rise to a transformation which assigns to any probability measure μ on G and any vertex w in the action tree of the group a new probability measure μ w . If the measure μ is self-similar in the sense that μ w is a convex combination of μ and the δ-measure at the group identity, then the asymptotic entropy of the random walk (G, μ) vanishes; therefore, the random walk is Liouville and the group G is amenable. We construct self-similar measures on several classes of self-similar groups, including the Grigorchuk group of intermediate growth." @default.
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- W2045706494 date "2005-10-01" @default.
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- W2045706494 title "MÜNCHHAUSEN TRICK AND AMENABILITY OF SELF-SIMILAR GROUPS" @default.
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- W2045706494 doi "https://doi.org/10.1142/s0218196705002694" @default.
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