@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},
year = {2006},
publisher = {Elsevier},
volume = {42},
number = {1},
doi = {10.1016/j.anihpb.2005.02.004},
zbl = {1102.60041},
language = {fr},
url = {https://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 - https://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 https://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
[1] , A lower estimate for central probabilities on polycyclic groups, Canad. J. Math. 44 (1992) 897-910. | Zbl | MR
[2] , Introduction to p-Adic Numbers and Valuation Theory, Academic Press, 1964. | Zbl | MR
[3] , , Groupes réductifs, Publ. Math. IHES 27 (1965) 55-150. | Zbl | MR | Numdam
[4] , Local Fields, Cambridge University Press, 1986. | Zbl | MR
[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. | Zbl | MR | Numdam
[7] , , On diagonal lower bounds for heat kernels on non-compact manifolds and Markov chains, Duke Math. J. 89 (1) (1997) 133-199. | Zbl | MR
[8] , , , A geometric approach to on-diagonal heat kernel lower bounds on groups, Ann. Inst. Fourier 51 (6) (2001) 1763-1827. | Zbl | MR | Numdam
[9] , Heat kernel upper bounds on a complete non-compact manifold, Rev. Mat. Iberoamericana 10 (2) (1994) 395-452. | Zbl | MR
[10] , Gaussian upper bounds for the heat kernel on arbitrary manifolds, J. Differential Geom. 45 (1) (1997) 33-52. | Zbl | MR
[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. | Zbl | MR
[12] , Croissance polynomiale et périodes des fonctions harmoniques, Bull. Soc. Math. France 101 (1973) 333-379. | Zbl | MR | Numdam
[13] , On heat kernels on Lie groups, Math. Z. 210 (1992) 593-605. | Zbl | MR
[14] , , Gaussian estimates for Markov chains and random walks on groups, Ann. Probab. 21 (1993) 673-709. | Zbl | MR
[15] , Lie Algebras, Interscience, 1962. | Zbl | MR
[16] , Growth of connected locally compact groups, J. Funct. Anal. 12 (1973) 113-127. | Zbl | MR
[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. | Zbl | MR
[19] , Følner sequences on polycyclic groups, Rev. Mat. Iberoamericana 11 (3) (1995) 675-686. | Zbl | MR
[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. | Zbl | MR
[22] , , On random walks on wreath products, Ann. Probab. 30 (2) (2002) 1-30. | Zbl | MR
[23] , , Random walks on finite rank solvable groups, J. Eur. Math. Soc. 4 (2003) 313-342. | Zbl | MR
[24] , On classes of p-adic Lie groups, New York J. Math. 5 (1999) 101-105. | Zbl | MR
[25] , Classical Harmonic Analysis and Locally Compact Groups, Oxford Math. Monograph, Oxford University Press, 1968. | Zbl | MR
[26] , Lie Algebras and Lie Groups, Benjamin, New York, 1965. | Zbl | MR
[27] , Linear algebraic groups, in: , (Eds.), Algebraic Geometry IV, Springer-Verlag, 1993. | Zbl | MR
[28] , Random walks on soluble groups, Bull. Sci. Math. 107 (1983) 337-344. | Zbl | MR
[29] , A potential theoritic property of soluble groups, Bull. Sci. Math. 108 (1983) 263-273. | Zbl | MR
[30] , Groups of superpolynomial growth, in: (Ed.), Harmonic Analysis (Sendai, 1990), ICM Satellite Conference Proceedings, Springer, 1991. | Zbl | MR
[31] , Diffusion on Lie groups, Canad. J. Math. 46 (2) (1994) 438-448. | Zbl | MR
[32] , Diffusion on Lie groups II, Canad. J. Math. 46 (5) (1994) 1073-1092. | Zbl | MR
[33] , Hardy-Littlewood theory on unimodular groups, Ann. Inst. H. Poincaré Probab. Statist. 31 (4) (1995) 669-688. | Zbl | MR | Numdam
[34] , The heat kernel on Lie groups, Rev. Mat. Iberoamericana 12 (1) (1996) 147-186. | Zbl | MR
[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. | Zbl | MR
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