It is shown in this paper that the transition kernels corresponding to simple random walks on certain unimodular solvable p-adic groups admit upper Gaussian estimates.
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Anker J.-Ph. (1992). Sharp estimates for some functions of the Laplacian on noncompact symmetric spaces. Duke Math. J. 65(2): 257–297
Anker J.-Ph., Damek E., Yacoub Ch. (1996). Spherical analysis on harmonic AN groups. Ann. Scuola Norm. Sup. Pisa, 23(4): 643–679 Academic Press, New York
Borel A., Tits J. (1965). Groupes réductifs. Publ. Math. IHES 27, 55–150
Cassels J.W.S. (1986). Local Fields. Cambridge University Press, Cambridge
Guivarc’h Y. (1973). Croissance Polynômiale et Périodes Des Fonctions Harmoniques. Bull. Soc. Math. Fr. 101, 333–379
Hebisch W., Saloff-Coste L. (1993). Gaussian estimates for Markov chains and random walks on groups. Ann. Probab. 21, 673–709
Mustapha S. (2005). Random walks on unimodular p-adic groups. Stoch. Process Appl. 115(6): 927–937
Pittet, Ch., and Saloff-Coste, L. (1999). Amenable Groups, Isoperimetric Profiles and Random Walks, Geometric Group Theory Down Under (Canberra, 1996), de Gruyter, Berlin, 293–316.
Pittet Ch., Saloff-Coste L. (2002). On random walks on wreath products. Ann. Probab. 30(2): 1–30
Raja C.R.E. (1999). On Classes of P-adic Lie Groups. New York J. Math. 5, 101–105
Revelle D. (2003). Heat kernel asymptotics on the lamplighter group. Electron. Comm. Probab. 8, 142–154
Taibleson, M. H. (1975). Fourier Analysis on Local Fields, Princeton University Press, Princeton, NJ, University of Tokyo Press, Tokyo.
Varopoulos N.Th. (1996). The Heat Kernel on Lie Groups. Rev. Mat. Iberoam. 12(1): 147–186
Varopoulos N.Th. (2000). Geometric and potential theoretic results on Lie groups. Canad. J. Math. 52(2): 412–437
Varopoulos N.Th., Saloff-Coste L., Coulhon Th. (1992). Analysis and Geometry on Groups, Camb. Tracts Mathemathics Vol. 100. Cambridge University Press, Cambridge
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Mustapha, S. Gaussian Estimates for Random Walks on Some Unimodular p-adic Groups. J Theor Probab 19, 773–787 (2006). https://doi.org/10.1007/s10959-006-0044-z
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DOI: https://doi.org/10.1007/s10959-006-0044-z