Geodesic
Subequivalence relations and positive-definite functions
Adrian Ioana1 orcid ; Alexander S. Kechris2 ; Todor Tsankov3
1University of California, San Diego, United States
2California Institute of Technology, Pasadena, United States
3Université Pierre et Marie Curie, Paris, France
Groups, geometry, and dynamics, Tome 3 (2009) no. 4, pp. 579-625

Voir la notice de l'article provenant de la source EMS Press

DOI

We study a positive-definite function associated with a countable, measure-preserving equivalence relation, which can be used to measure quantitatively the proximity of subequivalence relations. Combined with a co-inducing construction introduced by Epstein and earlier work of Ioana, this can be used to construct many mixing actions of countable groups and establish the non-classifiability, in a strong sense, of orbit equivalence of actions of non-amenable groups. We also discuss connections with percolation on Cayley graphs and the theory of costs.
DOI : 10.4171/ggd/71
Classification : 37-XX, 03-XX, 00-XX
Mots-clés : Subequivalence relations, positive-definite functions, co-induced action, orbit equivalence, non-amenable groups, classification, percolation, property (T), cost

Adrian Ioana  1   ; Alexander S. Kechris  2   ; Todor Tsankov  3

1 University of California, San Diego, United States
2 California Institute of Technology, Pasadena, United States
3 Université Pierre et Marie Curie, Paris, France 
Adrian Ioana; Alexander S. Kechris; Todor Tsankov. Subequivalence relations and positive-definite functions. Groups, geometry, and dynamics, Tome 3 (2009) no. 4, pp. 579-625. doi: 10.4171/ggd/71
@article{10_4171_ggd_71,
     author = {Adrian Ioana and Alexander S. Kechris and Todor Tsankov},
     title = {Subequivalence relations and positive-definite functions},
     journal = {Groups, geometry, and dynamics},
     pages = {579--625},
     year = {2009},
     volume = {3},
     number = {4},
     doi = {10.4171/ggd/71},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/71/}
}
TY  - JOUR
AU  - Adrian Ioana
AU  - Alexander S. Kechris
AU  - Todor Tsankov
TI  - Subequivalence relations and positive-definite functions
JO  - Groups, geometry, and dynamics
PY  - 2009
SP  - 579
EP  - 625
VL  - 3
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4171/ggd/71/
DO  - 10.4171/ggd/71
ID  - 10_4171_ggd_71
ER  - 
%0 Journal Article
%A Adrian Ioana
%A Alexander S. Kechris
%A Todor Tsankov
%T Subequivalence relations and positive-definite functions
%J Groups, geometry, and dynamics
%D 2009
%P 579-625
%V 3
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/71/
%R 10.4171/ggd/71
%F 10_4171_ggd_71

Cité par Sources :