Actions moyennables et fonctions harmoniques
Comptes Rendus. Mathématique, Tome 334 (2002) no. 5, pp. 355-358.

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

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

Reçu le :
Publié le :
DOI : 10.1016/S1631-073X(02)02276-8
Biane, Philippe 1 ; Germain, Emmanuel 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 = {Biane, Philippe and Germain, Emmanuel},
     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},
     url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02276-8/}
}
TY  - JOUR
AU  - Biane, Philippe
AU  - Germain, Emmanuel
TI  - Actions moyennables et fonctions harmoniques
JO  - Comptes Rendus. Mathématique
PY  - 2002
SP  - 355
EP  - 358
VL  - 334
IS  - 5
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/S1631-073X(02)02276-8/
DO  - 10.1016/S1631-073X(02)02276-8
LA  - fr
ID  - CRMATH_2002__334_5_355_0
ER  - 
%0 Journal Article
%A Biane, Philippe
%A Germain, Emmanuel
%T Actions moyennables et fonctions harmoniques
%J Comptes Rendus. Mathématique
%D 2002
%P 355-358
%V 334
%N 5
%I Elsevier
%U http://www.numdam.org/articles/10.1016/S1631-073X(02)02276-8/
%R 10.1016/S1631-073X(02)02276-8
%G fr
%F CRMATH_2002__334_5_355_0
Biane, Philippe; Germain, Emmanuel. Actions moyennables et fonctions harmoniques. Comptes Rendus. Mathématique, Tome 334 (2002) no. 5, pp. 355-358. doi : 10.1016/S1631-073X(02)02276-8. http://www.numdam.org/articles/10.1016/S1631-073X(02)02276-8/

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

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

[3] Baum, P.; Connes, A.; Higson, N. 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] Derriennic, Y. 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] Gromov, M. Spaces and questions, GAFA 2000, Tel Aviv, 1999

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

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

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

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

[11] Woess, W. 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] Woess, W. 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

Cité par Sources :