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Entrelacements de semi-groupes provenantde paires de Gelfand

Published online by Cambridge University Press:  15 October 2010

Philippe Biane*
Affiliation:
CNRS, France. [email protected]
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Abstract

On donne des exemples d'entrelacements entre semi-groupes markoviens obtenus au moyen de considérations de théorie des groupes sur les paires de Gelfand

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2011

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References

Biane, P., Quantum random walk on the dual of SU(n). Probab. Theory Relat. Fields 89 (1991) 117129. CrossRef
P. Biane, Minuscule weights and random walks on lattices, Quantum probability and related topics, QP-PQ VII. World Scientific Publishing, River Edge, NJ (1992) 51–65.
P. Biane, Intertwining of Markov semi-groups, some examples. in Séminaire de Probabilités XXIX. Lecture Notes in Math. 1613, Springer, Berlin (1995) 30–36.
P. Biane, Quantum Markov processes and group representations, Quantum probability communications, QP-PQ X. World Scientific Publishing, River Edge, NJ (1998) 53–72.
P. Biane, Le théorème de Pitman, le groupe quantique SUq(2), et une question de P.A. Meyer, In memoriam Paul-André Meyer, in Séminaire de Probabilités XXXIX. Lecture Notes in Math. 1874, Springer, Berlin (2006) 61–75.
Carmona, P., Petit, F. and Yor, M., Beta-gamma random variables and intertwining relations between certain Markov processes. Rev. Mat. Iberoamericana 14 (1998) 311367. CrossRef
F.M. Choucroun, Analyse harmonique des groupes d'automorphismes d'arbres de Bruhat-Tits. Mém. Soc. Math. France (N.S.) 58 (1994)
A. Connes, Noncommutative geometry. Academic Press, Inc., San Diego, CA (1994).
Dubédat, J., Reflected planar Brownian motions, intertwining relations and crossing probabilities. Ann. Inst. H. Poincaré Probab. Statist. 40 (2004) 539552. CrossRef
J. Faraut, Analyse sur les paires de Gelfand, in Analyse harmonique. Les Cours du CIMPA (1982).
Faraut, J. and Harzallah, K., Distances hilbertiennes invariantes sur un espace homogène. Ann. Inst. Fourier (Grenoble) 24 (1974) 171217. CrossRef
Gaveau, B., Principe de moindre action, propagation de la chaleur et estimées sous-elliptiques sur certains groupes nilpotents. Acta Math. 139 (1977) 95153. CrossRef
Hirsch, F. and Yor, M., Fractional intertwinings between two Markov semi-groups. Potential Anal. 31 (2009) 133146. CrossRef
Matsumoto, H. and Yor, M., An analogue of Pitman's 2MX theorem for exponential Wiener functionals. Part I. A time-inversion approach. Nagoya Math. J. 159 (2000) 125166. CrossRef
N. O'Connell, Directed polymers and the quantum Toda lattice. arXiv:0910.0069
K.R. Parthasarathy, An introduction to quantum stochastic calculus. Monographs Math. 85, Birkhäuser Verlag, Basel (1992).
Pitman, J.W., One-dimensional Brownian motion and the three-dimensional Bessel process. Adv. Appl. Probab. 7 (1975) 511526. CrossRef