Bornes inférieures pour les marches aléatoires sur les groupes p-adiques moyennables
Mustapha, Sami
Annales de l'I.H.P. Probabilités et statistiques, Tome 42 (2006), p. 81-88 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@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},
     volume = {42},
     year = {2006},
     pages = {81-88},
     doi = {10.1016/j.anihpb.2005.02.004},
     zbl = {1102.60041},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/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) pp. 81-88. doi : 10.1016/j.anihpb.2005.02.004. http://gdmltest.u-ga.fr/item/AIHPB_2006__42_1_81_0/

[1] G. Alexopoulos, A lower estimate for central probabilities on polycyclic groups, Canad. J. Math. 44 (1992) 897-910. | MR 1186471 | Zbl 0762.31003

[2] G. Bachman, Introduction to p-Adic Numbers and Valuation Theory, Academic Press, 1964. | MR 169847 | Zbl 0192.40103

[3] A. Borel, J. Tits, Groupes réductifs, Publ. Math. IHES 27 (1965) 55-150. | Numdam | MR 207712 | Zbl 0145.17402

[4] J.W.S. Cassels, Local Fields, Cambridge University Press, 1986. | MR 861410 | Zbl 0595.12006

[5] C. Chevalley, Théorie des Groupes de Lie, tome III, Hermann, 1955. | MR 68552

[6] Th. Coulhon, 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 1640375 | Zbl 1021.35014

[7] Th. Coulhon, A. Grigor'Yan, On diagonal lower bounds for heat kernels on non-compact manifolds and Markov chains, Duke Math. J. 89 (1) (1997) 133-199. | MR 1458975 | Zbl 0920.58064

[8] Th. Coulhon, A. Grigor'Yan, Ch. Pittet, A geometric approach to on-diagonal heat kernel lower bounds on groups, Ann. Inst. Fourier 51 (6) (2001) 1763-1827. | Numdam | MR 1871289 | Zbl 01710118

[9] A. Grigor'Yan, Heat kernel upper bounds on a complete non-compact manifold, Rev. Mat. Iberoamericana 10 (2) (1994) 395-452. | MR 1286481 | Zbl 0810.58040

[10] A. Grigor'Yan, Gaussian upper bounds for the heat kernel on arbitrary manifolds, J. Differential Geom. 45 (1) (1997) 33-52. | MR 1443330 | Zbl 0865.58042

[11] R.I. Grigorchuk, 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 764305 | Zbl 0583.20023

[12] Y. Guivarc'H, Croissance polynomiale et périodes des fonctions harmoniques, Bull. Soc. Math. France 101 (1973) 333-379. | Numdam | MR 369608 | Zbl 0294.43003

[13] W. Hebisch, On heat kernels on Lie groups, Math. Z. 210 (1992) 593-605. | MR 1175724 | Zbl 0792.22007

[14] W. Hebisch, L. Saloff-Coste, Gaussian estimates for Markov chains and random walks on groups, Ann. Probab. 21 (1993) 673-709. | MR 1217561 | Zbl 0776.60086

[15] N. Jacobson, Lie Algebras, Interscience, 1962. | MR 143793 | Zbl 0121.27504

[16] J. Jenkins, Growth of connected locally compact groups, J. Funct. Anal. 12 (1973) 113-127. | MR 349895 | Zbl 0247.43001

[17] S. Mustapha, Random walks on unimodular p-adic groups, Preprint. | MR 2134485

[18] S. Mustapha, Gaussian estimates for heat kernels on Lie groups, Math. Proc. Cambridge Philos. Soc. 128 (1) (2000) 45-64. | MR 1724427 | Zbl 0947.22007

[19] Ch. Pittet, Følner sequences on polycyclic groups, Rev. Mat. Iberoamericana 11 (3) (1995) 675-686. | MR 1363210 | Zbl 0842.20035

[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] Ch. Pittet, L. Saloff-Coste, Amenable groups, isoperimetric profiles and random walks, in: Geometric Group Theory Down Under (Canberra, 1996), de Gruyter, Berlin, 1999, pp. 293-316. | MR 1714851 | Zbl 0934.43001

[22] Ch. Pittet, L. Saloff-Coste, On random walks on wreath products, Ann. Probab. 30 (2) (2002) 1-30. | MR 1905862 | Zbl 1021.60004

[23] Ch. Pittet, L. Saloff-Coste, Random walks on finite rank solvable groups, J. Eur. Math. Soc. 4 (2003) 313-342. | MR 2017850 | Zbl 1057.20026

[24] C.R.E. Raja, On classes of p-adic Lie groups, New York J. Math. 5 (1999) 101-105. | MR 1703206 | Zbl 0923.22006

[25] H. Rieter, Classical Harmonic Analysis and Locally Compact Groups, Oxford Math. Monograph, Oxford University Press, 1968. | MR 306811 | Zbl 0165.15601

[26] J.-P. Serre, Lie Algebras and Lie Groups, Benjamin, New York, 1965. | MR 218496 | Zbl 0132.27803

[27] T.A. Springer, Linear algebraic groups, in: Parshin A.N., Shafarevich I.R. (Eds.), Algebraic Geometry IV, Springer-Verlag, 1993. | MR 1309681 | Zbl 0789.20044

[28] N.Th. Varopoulos, Random walks on soluble groups, Bull. Sci. Math. 107 (1983) 337-344. | MR 732356 | Zbl 0532.60009

[29] N.Th. Varopoulos, A potential theoritic property of soluble groups, Bull. Sci. Math. 108 (1983) 263-273. | MR 771912 | Zbl 0546.60008

[30] N.Th. Varopoulos, Groups of superpolynomial growth, in: Igasi S. (Ed.), Harmonic Analysis (Sendai, 1990), ICM Satellite Conference Proceedings, Springer, 1991. | MR 1261441 | Zbl 0802.43002

[31] N.Th. Varopoulos, Diffusion on Lie groups, Canad. J. Math. 46 (2) (1994) 438-448. | MR 1271225 | Zbl 0845.22006

[32] N.Th. Varopoulos, Diffusion on Lie groups II, Canad. J. Math. 46 (5) (1994) 1073-1092. | MR 1295132 | Zbl 0829.22013

[33] N.Th. Varopoulos, Hardy-Littlewood theory on unimodular groups, Ann. Inst. H. Poincaré Probab. Statist. 31 (4) (1995) 669-688. | Numdam | MR 1355612 | Zbl 0844.60006

[34] N.Th. Varopoulos, The heat kernel on Lie groups, Rev. Mat. Iberoamericana 12 (1) (1996) 147-186. | MR 1387589 | Zbl 0853.22006

[35] N.Th. Varopoulos, L. Saloff-Coste, Th. Coulhon, Analysis and Geomety on Groups, Cambridge Tracts in Math., vol. 102, Cambridge University Press, 1993. | MR 1218884

[36] W. Woess, Random Walks on Infinite Graphs and Groups, Cambridge Tracts in Math., vol. 138, Cambridge University Press, 2000. | MR 1743100 | Zbl 0951.60002