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151
Processes on unimodular random networks
, 2007
"... We investigate unimodular random networks. Our motivations include their characterization via reversibility of an associated random walk and their similarities to unimodular quasitransitive graphs. We extend various theorems concerning random walks, percolation, spanning forests, and amenability fr ..."
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Cited by 124 (6 self)
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We investigate unimodular random networks. Our motivations include their characterization via reversibility of an associated random walk and their similarities to unimodular quasitransitive graphs. We extend various theorems concerning random walks, percolation, spanning forests, and amenability from the known context of unimodular quasitransitive graphs to the more general context of unimodular random networks. We give properties of a trace associated to unimodular random networks with applications
UNIVERSAL CHARACTERISTIC FACTORS AND FURSTENBERG AVERAGES
, 2004
"... Let X = (X 0, B, µ, T) be an ergodic probability measure preserving system. For a natural number k we consider the averages N ∑ k ∏ 1 fj(T ..."
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Cited by 91 (6 self)
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Let X = (X 0, B, µ, T) be an ergodic probability measure preserving system. For a natural number k we consider the averages N ∑ k ∏ 1 fj(T
On exchangeable random variables and the statistics of large graphs and hypergraphs
, 2008
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Analytic equivalence relations and Ulmtype classifications
 J. SYMBOLIC LOGIC
, 1995
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A topological version of the Bergman property
"... ABSTRACT. A topological group G is defined to have property (OB) if any Gaction by isometries on a metric space, which is separately continuous, has bounded orbits. We study this topological analogue of strong uncountable cofinality in the context of Polish groups, where we show it to have several ..."
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Cited by 24 (10 self)
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ABSTRACT. A topological group G is defined to have property (OB) if any Gaction by isometries on a metric space, which is separately continuous, has bounded orbits. We study this topological analogue of strong uncountable cofinality in the context of Polish groups, where we show it to have several interesting reformulations and consequences. We subsequently apply the results obtained in order to verify property (OB) for a number of groups of isometries and homeomorphism groups of compact metric spaces. We also give a proof that the isometry group of the rational Urysohn metric space of diameter 1 has strong uncountable cofinality. 1.
On the Complexity of the Isomorphism Relation for Finitely Generated Groups
, 1998
"... Working within the framework of descriptive set theory, we show that the isomorphism relation for finitely generated groups is a universal essentially countable Borel equivalence relation. We also prove the corresponding result for the conjugacy relation for subgroups of the free group on two genera ..."
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Cited by 24 (11 self)
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Working within the framework of descriptive set theory, we show that the isomorphism relation for finitely generated groups is a universal essentially countable Borel equivalence relation. We also prove the corresponding result for the conjugacy relation for subgroups of the free group on two generators. The proofs are grouptheoretic, and we refer to descriptive set theory only for the relevant definitions and for motivation for the results. Introduction Given a class K of structures for a fixed first order language L, one may ask what kinds of complete invariants can be used to classify the elements of K up to isomorphism. For those classes consisting of the countable models of some L ! 1 ;! sentence, Friedman and Stanley [FS] proposed to use the methods of descriptive set theory to study their possible invariants and defined the notion of Borel reducibility between such classes of structures. In [HK], Hjorth and Kechris continued this study and situated it within the general the...