منابع مشابه
Unimodularity of Invariant Random Subgroups
An invariant random subgroup H ≤ G is a random closed subgroup whose law is invariant to conjugation by all elements of G. When G is locally compact and second countable, we show that for every invariant random subgroup H ≤ G there almost surely exists an invariant measure on G/H. Equivalently, the modular function of H is almost surely equal to the modular function of G, restricted to H. We us...
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An invariant random subgroup of the countable group Γ is a random subgroup of Γ whose distribution is invariant under conjugation by all elements of Γ. We prove that for a nonamenable invariant random subgroup H , the spectral radius of every finitely supported random walk on Γ is strictly less than the spectral radius of the corresponding random walk on Γ/H . This generalizes a result of Keste...
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Let G be a countably infinite group and (X,μ) a standard non-atomic probability space. We denote by A(G,X, μ) the space of measure preserving actions of G on (X,μ) with the weak topology. If a,b ∈ A(G,X, μ), we say that a is weakly contained in b, in symbols a b, if a is in the closure of the set of isomorphic copies of b (i.e., it is in the closure of the orbit of b under the action of the aut...
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We consider groups of automorphisms of locally finite trees, and give conditions on its subgroups that imply that they are not elementary amenable. This covers all known examples of groups that are not elementary amenable and act on the trees: groups of intermediate growths and Basilica group, by giving a more straightforward proof. Moreover, we deduce that all finitely generated branch groups ...
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2016
ISSN: 0021-2172,1565-8511
DOI: 10.1007/s11856-016-1324-7