[Approximations de relations d'équivalence standard et percolation de Bernoulli à pu]
Le but de cette note est d'annoncer certains résultats d'équivalence orbitale, concernant notamment la notion d'approximation de relations d'équivalence standard préservant la mesure de probabilité par suites croissantes de sous-relations, avec application au comportement en de la percolation de Bernoulli sur les graphes de Cayley.
The goal of this note is to announce certain results in orbit equivalence theory, especially concerning the approximation of p.m.p. standard equivalence relations by increasing sequences of sub-relations, with application to the behavior of the Bernoulli percolation on Cayley graphs at the threshold .
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@article{CRMATH_2016__354_11_1114_0,
author = {Gaboriau, Damien and Tucker-Drob, Robin},
title = {Approximations of standard equivalence relations and {Bernoulli} percolation at \protect\emph{p}\protect\textsubscript{\protect\emph{u}}},
journal = {Comptes Rendus. Math\'ematique},
pages = {1114--1118},
publisher = {Elsevier},
volume = {354},
number = {11},
year = {2016},
doi = {10.1016/j.crma.2016.09.011},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2016.09.011/}
}
TY - JOUR AU - Gaboriau, Damien AU - Tucker-Drob, Robin TI - Approximations of standard equivalence relations and Bernoulli percolation at pu JO - Comptes Rendus. Mathématique PY - 2016 SP - 1114 EP - 1118 VL - 354 IS - 11 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2016.09.011/ DO - 10.1016/j.crma.2016.09.011 LA - en ID - CRMATH_2016__354_11_1114_0 ER -
%0 Journal Article %A Gaboriau, Damien %A Tucker-Drob, Robin %T Approximations of standard equivalence relations and Bernoulli percolation at pu %J Comptes Rendus. Mathématique %D 2016 %P 1114-1118 %V 354 %N 11 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2016.09.011/ %R 10.1016/j.crma.2016.09.011 %G en %F CRMATH_2016__354_11_1114_0
Gaboriau, Damien; Tucker-Drob, Robin. Approximations of standard equivalence relations and Bernoulli percolation at pu. Comptes Rendus. Mathématique, Tome 354 (2016) no. 11, pp. 1114-1118. doi : 10.1016/j.crma.2016.09.011. http://www.numdam.org/articles/10.1016/j.crma.2016.09.011/
[1] Ergodic equivalence relations, cohomology, and von Neumann algebras. I, Trans. Amer. Math. Soc., Volume 234 (1977) no. 2, pp. 289-324
[2] Invariants de relations d'équivalence et de groupes, Publ. Math. Inst. Hautes Études Sci., Volume 95 (2002), pp. 93-150
[3] Invariant percolation and harmonic Dirichlet functions, Geom. Funct. Anal., Volume 15 (2005) no. 5, pp. 1004-1051
[4] D. Gaboriau, R. Tucker-Drob, Approximations and dimensions of standard equivalence relations, in preparation.
[5] Monotonicity of uniqueness for percolation on Cayley graphs: all infinite clusters are born simultaneously, Probab. Theory Relat. Fields, Volume 113 (1999) no. 2, pp. 273-285
[6] Sub-equivalence relations and positive-definite functions, Groups Geom. Dyn., Volume 3 (2009) no. 4, pp. 579-625
[7] Asymptotically invariant sequences and approximate finiteness, Amer. J. Math., Volume 109 (1987) no. 1, pp. 91-114
[8] Probability on Trees and Networks, Cambridge University Press, New York, 2017 (pp. xvi + 699)
[9] Indistinguishability of percolation clusters, Ann. Probab., Volume 27 (1999) no. 4, pp. 1809-1836
[10] Ergodic theory of amenable group actions. I. The Rohlin lemma, Bull. Amer. Math. Soc. (N.S.), Volume 2 (1980) no. 1, pp. 161-164
[11] Percolation on nonamenable products at the uniqueness threshold, Ann. Inst. Henri Poincaré Probab. Stat., Volume 36 (2000) no. 3, pp. 395-406
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