Permutation model for semi-circular systems and quantum random walks

Pacific Journal of Mathematics

Volumn 171, Issue 2, 1995, Pages 373-387

  Biane, Philippe ^a  

^a University of Paris VII LPSM partially supported by ERC Starting Grant 680275 MALIG   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84972561053     PISSN: 00308730     EISSN: None     Source Type: Journal    
DOI: 10.2140/pjm.1995.171.373     Document Type: Article

References (18)

1. P. Bérard and G. Besson, Spectres et groupes cristallographiques II, Ann. Inst. Fourier, 30 (3) (1980), 237-248.
2. Ph. Biane, Quantum random walk on the dual of SU(n), Prob. Th. and Rel. Fields, 89 (1991), 117-129.
3. Ph. Biane, Some properties of quantum Bernoulli random walks, Quantum probability and applications 6, L. Accardi, W. von Waldenfels ed., World scientific, 1991, 193-204.
4. J.L. Doob, Classical potential theory and its probabilistic counterparty Springer Verlag, Berlin, Heidelberg, New York, 1984.
5. F. J. Dyson, A brownian motion model for the eigenvalues of a random matrix, Journ. Math. Phys., 3 (1962), 1191-1198.
6. N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes y North holland, Kodansha, 1981.
7. J. Jacod and A.N. Shyriaev, Limit theorems for stochastic processes, Springer, 1987.
8. G. Kreweras, Sur les partitions non croisées d’un cycle Discrete Math., 1 (1972).
9. H. P. Mac Kean, Stochastic integralsy Academic press, New York, 1969.
10. K. R. Parthasarathy, A generalized Biane’s process, Séminaire de probabilités XXIV, Springer Lecture Notes in Mathematics, 1426 (1990), 345-348.
11. J.W. Pitman, One dimensionnai brownian motion and the three dimensionnai Bessel procesSy Adv. Appl. Prob., 7 (1975), 511-526.
12. M. Schürmann, Quantum stochastic processes with independent additive incrementSy Jour. Multivariate Anal., 38 (1991), 15-35.
13. G. Skandalis, Algèbres de von Neumann de groupes libres et probabilités non commutatives [d’après Voiculescu et al.] y Séminaire Bourbaki, exposé 764, Novembre 1992.
14. R. Speicher, A new example of independence and white noise, Prob. Th. and Rel. Fields, 84 (1990), 141-159.
15. D. Voiculescu, Symmetries of some reduced free product C*-algebras, Operator algebras and their connection with topology and ergodic theory. Lect. Notes in Math. Springer, 1985, 556-588.
16. D. Voiculescu, Circular and semi-circular systems and free product factors, Operator algebras, Unitary representations, envelopping algebras, and invariant theory, Progress in Mathematics, Volume 92, Birkhaiiser, Boston, 1990.
17. D. Voiculescu, Limit laws for random matrices and free products, Invent. Math., 104 (1991), 201-220.
18. E.P. Wigner, Characteristic vectors of bordered matrices with infinite dimensions, Ann. Math., 62 (1955), 548-564.