Agenda de l’IDP

Séminaire Orléans

Limit theorems for random walks associated with hypergeometric functions of type BC
Michael Voit (Dortmund)
Thursday 19 March 2015 14:00 -  Orléans -  Salle de Séminaire

Résumé :
Consider the noncompact and compact Grassmann manifolds G_{p,q}(F) = G/K over the fields F = R, C, H with rank q and second dimension parameter p > q. The double coset spaces K\G/K can be identified with the corresponding Weyl chamber (or alcove in the compact case) C_q ⊂ R^q , and the spherical functions are Heckman-Opdam hypergeometric functions of type BC depending on the discrete parameter p. For p ≥ 2 q − 1 , the product formula and the Harish-Chandra integral representation for these spherical functions on C_q can be written explicitly in such a way that the resulting formulae can be extended to all real parameters p ∈ [ 2 q − 1, ∞ [. This leads to associated convolution structures and a notion of random walks on C_q for these p. We shall present some limit theorems for such random walks with explicit formulae for the drift and diffusion constants. In the group cases with integers p, these results have interpretations for G-invariant random walks on the Grassmannians G_{p,q}(F) and are, at least partially, known for a long time.

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