Etude analytique et probabiliste de laplaciens associés à des systèmes de racines :
laplacien hypergéométrique de Heckman--Opdam et laplacien combinatoire sur les immeubles affines.

Abstract : In this thesis, we are interested in
the study of analytical and probabilistic aspects of
Heckman--Opdam and affine buildings of type $\tilde{A}_r$
theories. We also study the Poisson boundary of rational
triangular matrices.

One of our main results, is to obtain new estimates of the
hypergeometric functions of Heckman--Opdam. Our proofs are
relatively more elementary than in the particular case of
symmetric spaces $G/K$. For instance for the proof of the basic
estimates of spherical functions, obtained by Harish-Chandra or
Gangolli and Varadarajan, and for the recent estimate of the
elementary spherical function $\phi_0$ by Anker, Bougerol and
Jeulin.

Another main result is the estimate of the heat kernel associated
with some combinatorial Laplacian on an affine building of
type $\tilde{A}_r$.
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Theses
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Submitted on : Tuesday, November 21, 2006 - 6:05:33 PM
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Bruno Schapira. Etude analytique et probabiliste de laplaciens associés à des systèmes de racines :
laplacien hypergéométrique de Heckman--Opdam et laplacien combinatoire sur les immeubles affines.. Mathématiques [math]. Université d'Orléans, 2006. Français. ⟨tel-00115557⟩

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