@article{AIHPB_2006__42_1_81_0, author = {Mustapha, Sami}, title = {Bornes inf\'erieures pour les marches al\'eatoires sur les groupes $p$-adiques moyennables}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {81--88}, publisher = {Elsevier}, volume = {42}, number = {1}, year = {2006}, doi = {10.1016/j.anihpb.2005.02.004}, zbl = {1102.60041}, language = {fr}, url = {http://www.numdam.org/articles/10.1016/j.anihpb.2005.02.004/} }
TY - JOUR AU - Mustapha, Sami TI - Bornes inférieures pour les marches aléatoires sur les groupes $p$-adiques moyennables JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2006 SP - 81 EP - 88 VL - 42 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpb.2005.02.004/ DO - 10.1016/j.anihpb.2005.02.004 LA - fr ID - AIHPB_2006__42_1_81_0 ER -
%0 Journal Article %A Mustapha, Sami %T Bornes inférieures pour les marches aléatoires sur les groupes $p$-adiques moyennables %J Annales de l'I.H.P. Probabilités et statistiques %D 2006 %P 81-88 %V 42 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpb.2005.02.004/ %R 10.1016/j.anihpb.2005.02.004 %G fr %F AIHPB_2006__42_1_81_0
Mustapha, Sami. Bornes inférieures pour les marches aléatoires sur les groupes $p$-adiques moyennables. Annales de l'I.H.P. Probabilités et statistiques, Tome 42 (2006) no. 1, pp. 81-88. doi : 10.1016/j.anihpb.2005.02.004. http://www.numdam.org/articles/10.1016/j.anihpb.2005.02.004/
[1] A lower estimate for central probabilities on polycyclic groups, Canad. J. Math. 44 (1992) 897-910. | MR | Zbl
,[2] Introduction to p-Adic Numbers and Valuation Theory, Academic Press, 1964. | MR | Zbl
,[3] Groupes réductifs, Publ. Math. IHES 27 (1965) 55-150. | Numdam | MR | Zbl
, ,[4] Local Fields, Cambridge University Press, 1986. | MR | Zbl
,[5] Théorie des Groupes de Lie, tome III, Hermann, 1955. | MR
,[6] Large time behaviour of heat kernels on Riemannian manifolds: fast and slow decays, in: Journées équations aux dérivées partielles, St-Jean-de-Monts, 1998, pp. 1-12. | Numdam | MR | Zbl
,[7] On diagonal lower bounds for heat kernels on non-compact manifolds and Markov chains, Duke Math. J. 89 (1) (1997) 133-199. | MR | Zbl
, ,[8] A geometric approach to on-diagonal heat kernel lower bounds on groups, Ann. Inst. Fourier 51 (6) (2001) 1763-1827. | Numdam | MR | Zbl
, , ,[9] Heat kernel upper bounds on a complete non-compact manifold, Rev. Mat. Iberoamericana 10 (2) (1994) 395-452. | MR | Zbl
,[10] Gaussian upper bounds for the heat kernel on arbitrary manifolds, J. Differential Geom. 45 (1) (1997) 33-52. | MR | Zbl
,[11] Degrees of growth of finitely generated groups and the theory of invariant means, Izv. Akad. Nauk SSSR Ser. Mat. 49 (5) (1984) 939-985, English translation: Math. USSR-Izv. 25 (1985), 259-300. | MR | Zbl
,[12] Croissance polynomiale et périodes des fonctions harmoniques, Bull. Soc. Math. France 101 (1973) 333-379. | Numdam | MR | Zbl
,[13] On heat kernels on Lie groups, Math. Z. 210 (1992) 593-605. | MR | Zbl
,[14] Gaussian estimates for Markov chains and random walks on groups, Ann. Probab. 21 (1993) 673-709. | MR | Zbl
, ,[15] Lie Algebras, Interscience, 1962. | MR | Zbl
,[16] Growth of connected locally compact groups, J. Funct. Anal. 12 (1973) 113-127. | MR | Zbl
,[17] S. Mustapha, Random walks on unimodular p-adic groups, Preprint. | MR
[18] Gaussian estimates for heat kernels on Lie groups, Math. Proc. Cambridge Philos. Soc. 128 (1) (2000) 45-64. | MR | Zbl
,[19] Følner sequences on polycyclic groups, Rev. Mat. Iberoamericana 11 (3) (1995) 675-686. | MR | Zbl
,[20] Ch. Pittet, L. Saloff-Coste, A survey on the relationship between volume growth, isoperimetry, and the behavior of simple random walk on Cayley graphs, with examples, Preprint, 1997.
[21] Amenable groups, isoperimetric profiles and random walks, in: Geometric Group Theory Down Under (Canberra, 1996), de Gruyter, Berlin, 1999, pp. 293-316. | MR | Zbl
, ,[22] On random walks on wreath products, Ann. Probab. 30 (2) (2002) 1-30. | MR | Zbl
, ,[23] Random walks on finite rank solvable groups, J. Eur. Math. Soc. 4 (2003) 313-342. | MR | Zbl
, ,[24] On classes of p-adic Lie groups, New York J. Math. 5 (1999) 101-105. | MR | Zbl
,[25] Classical Harmonic Analysis and Locally Compact Groups, Oxford Math. Monograph, Oxford University Press, 1968. | MR | Zbl
,[26] Lie Algebras and Lie Groups, Benjamin, New York, 1965. | MR | Zbl
,[27] Linear algebraic groups, in: , (Eds.), Algebraic Geometry IV, Springer-Verlag, 1993. | MR | Zbl
,[28] Random walks on soluble groups, Bull. Sci. Math. 107 (1983) 337-344. | MR | Zbl
,[29] A potential theoritic property of soluble groups, Bull. Sci. Math. 108 (1983) 263-273. | MR | Zbl
,[30] Groups of superpolynomial growth, in: (Ed.), Harmonic Analysis (Sendai, 1990), ICM Satellite Conference Proceedings, Springer, 1991. | MR | Zbl
,[31] Diffusion on Lie groups, Canad. J. Math. 46 (2) (1994) 438-448. | MR | Zbl
,[32] Diffusion on Lie groups II, Canad. J. Math. 46 (5) (1994) 1073-1092. | MR | Zbl
,[33] Hardy-Littlewood theory on unimodular groups, Ann. Inst. H. Poincaré Probab. Statist. 31 (4) (1995) 669-688. | Numdam | MR | Zbl
,[34] The heat kernel on Lie groups, Rev. Mat. Iberoamericana 12 (1) (1996) 147-186. | MR | Zbl
,[35] Analysis and Geomety on Groups, Cambridge Tracts in Math., vol. 102, Cambridge University Press, 1993. | MR
, , ,[36] Random Walks on Infinite Graphs and Groups, Cambridge Tracts in Math., vol. 138, Cambridge University Press, 2000. | MR | Zbl
,Cité par Sources :