Entrelacements de semi-groupes provenant de paires de Gelfand
ESAIM: Probability and Statistics, Tome 15 (2011), pp. S2-S10.

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

DOI : 10.1051/ps/2010025
Classification : 60J23, 60J35, 22D15
Mots-clés : entrelacement de semi-groupes de noyaux markoviens, paires de Gelfand
@article{PS_2011__15__S2_0,
     author = {Biane, Philippe},
     title = {Entrelacements de semi-groupes provenant de paires de {Gelfand}},
     journal = {ESAIM: Probability and Statistics},
     pages = {S2--S10},
     publisher = {EDP-Sciences},
     volume = {15},
     year = {2011},
     doi = {10.1051/ps/2010025},
     mrnumber = {2817341},
     language = {fr},
     url = {http://www.numdam.org/articles/10.1051/ps/2010025/}
}
TY  - JOUR
AU  - Biane, Philippe
TI  - Entrelacements de semi-groupes provenant de paires de Gelfand
JO  - ESAIM: Probability and Statistics
PY  - 2011
SP  - S2
EP  - S10
VL  - 15
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ps/2010025/
DO  - 10.1051/ps/2010025
LA  - fr
ID  - PS_2011__15__S2_0
ER  - 
%0 Journal Article
%A Biane, Philippe
%T Entrelacements de semi-groupes provenant de paires de Gelfand
%J ESAIM: Probability and Statistics
%D 2011
%P S2-S10
%V 15
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ps/2010025/
%R 10.1051/ps/2010025
%G fr
%F PS_2011__15__S2_0
Biane, Philippe. Entrelacements de semi-groupes provenant de paires de Gelfand. ESAIM: Probability and Statistics, Tome 15 (2011), pp. S2-S10. doi : 10.1051/ps/2010025. http://www.numdam.org/articles/10.1051/ps/2010025/

[1] P. Biane, Quantum random walk on the dual of SU(n). Probab. Theory Relat. Fields 89 (1991) 117-129. | MR | Zbl

[2] 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. | MR | Zbl

[3] P. Biane, Intertwining of Markov semi-groups, some examples. in Séminaire de Probabilités XXIX. Lecture Notes in Math. 1613, Springer, Berlin (1995) 30-36. | EuDML | Numdam | MR | Zbl

[4] P. Biane, Quantum Markov processes and group representations, Quantum probability communications, QP-PQ X. World Scientific Publishing, River Edge, NJ (1998) 53-72. | MR

[5] 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. | MR | Zbl

[6] P. Carmona, F. Petit and M. Yor, Beta-gamma random variables and intertwining relations between certain Markov processes. Rev. Mat. Iberoamericana 14 (1998) 311-367. | EuDML | MR | Zbl

[7] F.M. Choucroun, Analyse harmonique des groupes d'automorphismes d'arbres de Bruhat-Tits. Mém. Soc. Math. France (N.S.) 58 (1994) | EuDML | Numdam | MR | Zbl

[8] A. Connes, Noncommutative geometry. Academic Press, Inc., San Diego, CA (1994). | MR | Zbl

[9] J. Dubédat, Reflected planar Brownian motions, intertwining relations and crossing probabilities. Ann. Inst. H. Poincaré Probab. Statist. 40 (2004) 539-552. | EuDML | Numdam | MR | Zbl

[10] J. Faraut, Analyse sur les paires de Gelfand, in Analyse harmonique. Les Cours du CIMPA (1982).

[11] J. Faraut and K. Harzallah, Distances hilbertiennes invariantes sur un espace homogène. Ann. Inst. Fourier (Grenoble) 24 (1974) 171-217. | EuDML | Numdam | MR | Zbl

[12] B. Gaveau, Principe de moindre action, propagation de la chaleur et estimées sous-elliptiques sur certains groupes nilpotents. Acta Math. 139 (1977) 95-153. | MR | Zbl

[13] F. Hirsch and M. Yor, Fractional intertwinings between two Markov semi-groups. Potential Anal. 31 (2009) 133-146. | MR | Zbl

[14] H. Matsumoto and M. Yor, An analogue of Pitman's 2M - X theorem for exponential Wiener functionals. Part I. A time-inversion approach. Nagoya Math. J. 159 (2000) 125-166. | MR | Zbl

[15] N. O'Connell, Directed polymers and the quantum Toda lattice. arXiv:0910.0069 | MR | Zbl

[16] K.R. Parthasarathy, An introduction to quantum stochastic calculus. Monographs Math. 85, Birkhäuser Verlag, Basel (1992). | MR | Zbl

[17] J.W. Pitman, One-dimensional Brownian motion and the three-dimensional Bessel process. Adv. Appl. Probab. 7 (1975) 511-526. | MR | Zbl

Cité par Sources :