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Recall that two ergodic probability measure preserving (p.m.p.) actions σi for i = 1, 2 of two countable groups Γi on probability measure standard Borel spaces (Xi, μi) are orbit equivalent (OE) if they define partitions of the spaces into orbits that are isomorphic, more precisely, if there exists a measurable, almost everywhere defined isomorphism f : X1… (More)

- Damien Gaboriau
- 2004

The main goal of this paper is to answer question 1.10 and settle conjecture 1.11 of BenjaminiLyons-Schramm [BLS99] relating harmonic Dirichlet functions on a graph to those on the infinite clusters in the uniqueness phase of Bernoulli percolation. We extend the result to more general invariant percolations, including the Random-Cluster model. We prove the… (More)

We give a positive answer, in the measurable-group-theory context, to von Neumann’s problem of knowing whether a non-amenable countable discrete group contains a non-cyclic free subgroup. We also get an embedding result of the free-group von Neumann factor into restricted wreath product factors. 2000 Mathematical Subject Classification: 37A20, 20E05, 82B43,… (More)

- Damien Gaboriau
- 2005

Measure Equivalence (ME) is the measure theoretic counterpart of quasi-isometry. This field grew considerably during the last years, developing tools to distinguish between different ME classes of countable groups. On the other hand, contructions of ME equivalent groups are very rare. We present a new method, based on a notion of measurable free-factor, and… (More)

- Raphaëlle Tourdot-Maréchal, Damien Gaboriau, Laurent Beney, Charles Diviès
- International journal of food microbiology
- 2000

The determination of membrane fluidity in whole cells of Oenococcus oeni was achieved by membrane probe 1,6-diphenyl-1,3,5-hexatriene fluorescence anisotropy measurements. The results demonstrated instantaneous fluidity variations with cells directly stressed during the measure. Heat (42 degrees C) or acid (pH 3.2) shocks decreased the anisotropy values… (More)

- ET DE GROUPES, Damien Gaboriau
- 2002

On s’intéresse à une étude géométrico-ergodique des groupes discrets dénombrables, en particulier aux liens entre les nombres de Betti 2 des groupes et leurs actions mesurables préservant une mesure. On en déduit d’une part des résultats sur la classification des relations d’équivalence standards et d’autre part des résultats sur les nombres de Betti 2 des… (More)

- Damien Gaboriau
- 2010

We give a survey of various recent developments in orbit equivalence and measured group theory. This subject aims at studying infinite countable groups through their measure preserving actions. 2000 Mathematical Subject Classification: Primary 37A20; Secondary 46L10; 28D15.

- Damien Gaboriau
- 2005

Measure Equivalence (ME) is the measure theoretic counterpart of quasi-isometry. This field grew considerably during the last years, developing tools to distinguish between different ME classes of countable groups. On the other hand, contructions of ME equivalent groups are very rare. We present a new method, based on a notion of measurable free-factor, and… (More)

- Damien Gaboriau
- 2009

We show that every non-amenable free product of groups admits free ergodic probability measure preserving actions which have relative property (T) in the sense of S. Popa [Pop06, Def. 4.1]. There are continuum many such actions up to orbit equivalence and von Neumann equivalence, and they may be chosen to be conjugate to any prescribed action when… (More)

We study the analogue in orbit equivalence of free product decomposition and free indecomposability for countable groups. We introduce the (orbit equivalence invariant) notion of freely indecomposable (FI) standard probability measure preserving equivalence relations and establish a criterion to check it, namely non-hyperfiniteness and vanishing of the… (More)