Comptes Rendus
no. 5
Actions moyennables et fonctions harmoniques
[Ameanable actions and harmonic functions]
Philippe Biane1; Emmanuel Germain2
1 CNRS, Département de mathématiques et applications, École normale supérieure, 45, rue d'Ulm, 75005 Paris, France
2 Institut de mathématiques de Jussieu, Université Paris VII, 175, rue du Chevaleret, 75013 Paris, France
Comptes Rendus. Mathématique, Volume 334 (2002) no. 5, pp. 355-358.

We prove that the action of a countable discrete group on a locally compact invariant space of minimal harmonic functions is ameanable.

On montre que l'action d'un groupe dénombrable discret sur un espace localement compact invariant de fonctions harmoniques minimales est moyennable.

Received:
Published online:
DOI: 10.1016/S1631-073X(02)02276-8

Philippe Biane 1; Emmanuel Germain 2

1 CNRS, Département de mathématiques et applications, École normale supérieure, 45, rue d'Ulm, 75005 Paris, France
2 Institut de mathématiques de Jussieu, Université Paris VII, 175, rue du Chevaleret, 75013 Paris, France 
@article{CRMATH_2002__334_5_355_0,
     author = {Philippe Biane and Emmanuel Germain},
     title = {Actions moyennables et fonctions harmoniques},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {355--358},
     publisher = {Elsevier},
     volume = {334},
     number = {5},
     year = {2002},
     doi = {10.1016/S1631-073X(02)02276-8},
     language = {fr},
}
TY  - JOUR
AU  - Philippe Biane
AU  - Emmanuel Germain
TI  - Actions moyennables et fonctions harmoniques
JO  - Comptes Rendus. Mathématique
PY  - 2002
SP  - 355
EP  - 358
VL  - 334
IS  - 5
PB  - Elsevier
DO  - 10.1016/S1631-073X(02)02276-8
LA  - fr
ID  - CRMATH_2002__334_5_355_0
ER  - 
%0 Journal Article
%A Philippe Biane
%A Emmanuel Germain
%T Actions moyennables et fonctions harmoniques
%J Comptes Rendus. Mathématique
%D 2002
%P 355-358
%V 334
%N 5
%I Elsevier
%R 10.1016/S1631-073X(02)02276-8
%G fr
%F CRMATH_2002__334_5_355_0
Philippe Biane; Emmanuel Germain. Actions moyennables et fonctions harmoniques. Comptes Rendus. Mathématique, Volume 334 (2002) no. 5, pp. 355-358. doi : 10.1016/S1631-073X(02)02276-8. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02276-8/

[1] C. Anantharaman; J. Renault Groupoı̈des moyennables, Monograph. Enseign. Math., 36, Genève, 2000

[2] A. Ancona Positive harmonic functions and hyperbolicity, Potential Theory – Surveys and Problems, Prague, 1987, Lecture Notes in Math., 1344, Springer, 1988, pp. 1-23

[3] P. Baum; A. Connes; N. Higson Classifying space for proper group actions an K-theory of group C * -algebras, Contemp. Math., Volume 167 (1994), pp. 241-291

[4] N.P. Brown, E. Germain, Dual entropy in discrete groups with amenable actions, Ergodic Theory Dynamical Systems (to appear)

[5] Y. Derriennic Lois « zéro ou deux » pour les processus de Markov. Applications aux marches aléatoires, Ann. Inst. H. Poincaré Sect. B (N.S.), Volume 12 (1976) no. 2, pp. 111-129

[6] M. Gromov Spaces and questions, GAFA 2000, Tel Aviv, 1999

[7] Y. Guivar'ch; L. Ji; J.C. Taylor Compactifications of Symetric Spaces, Birkhäuser, 1998

[8] J.G. Kemeny; J.L. Snell; A.W. Knapp Denumerable Markov Chains, Graduate Texts in Math., 40, Springer-Verlag, New York, 1976 (With a chapter on Markov random fields, by David Griffeath)

[9] J.-L. Tu Remarks on Yu's property A, Bull. Soc. Math. France, Volume 129 (2001), pp. 115-139

[10] S. Wassermann Exact C * -algebras and related topics, Seoul National University Global Analysis Research Center Lecture Notes, Volume 19 (1994)

[11] W. Woess Random walks on infinite graphs and groups – a survey on selected topics, Bull. London Math. Soc., Volume 26 (1994) no. 1, pp. 1-60

[12] W. Woess A description of the Martin boundary for nearest neighbour random walk on free products, Probability Measures on Groups, Oberwolfach, 1985, Lecture Notes in Math., 1210, Springer, Berlin, 1986, pp. 203-215

Cited by Sources:

Comments - Policy