Pacific Journal of Mathematics

Permutation model for semi-circular systems and quantum random walks.

Philippe Biane

Article information

Source
Pacific J. Math., Volume 171, Number 2 (1995), 373-387.

Dates
First available in Project Euclid: 6 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102368921

Mathematical Reviews number (MathSciNet)
MR1372234

Zentralblatt MATH identifier
0854.60070

Subjects
Primary: 46L50
Secondary: 60J65: Brownian motion [See also 58J65] 81S25: Quantum stochastic calculus

Citation

Biane, Philippe. Permutation model for semi-circular systems and quantum random walks. Pacific J. Math. 171 (1995), no. 2, 373--387. https://projecteuclid.org/euclid.pjm/1102368921


Export citation

References

  • [1] P. Berard 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 counterpart, Springer Ver- lag, 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 equationsand diffusion processes, North holland, Kodansha, 1981.
  • [7] J. Jacod and A.N. Shyriaev, Limit theoremsfor stochasticprocesses, Springer, 1987.
  • [8] G. Kreweras, Sur les partitions non croisees d'un cycleDiscrete Math., 1 (1972).
  • [9] H.P. Mac Kean, Stochastic integrals, Academic press, New York, 1969.
  • [10] K.R. Parthasarathy, A generalized Biane's process, Seminaire de probability's XXIV, Springer Lecture Notes in Mathematics, 1426 (1990), 345-348.
  • [11] J.W. Pitman One dimensionnal brownian motion and the three dimensionnal Bessel process, Adv. Appl. Prob., 7 (1975), 511-526.
  • [12] M. Schrmann, Quantum stochasticprocesseswith independent additive increments, Jour. Multivariate Anal, 38 (1991), 15-35.
  • [13] G. Skandalis, Algebresde von Neumann de groupeslibres et probabilitesnon com- mutatives [d'apres Voiculescuet al.], Seminaire Bourbaki, expose 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 productC* -algebras, Operator alge- bras and their connection with topology and ergodic theory. Lect. Notes in Math. Springer, 1985, 556-588.
  • [16] D. Voiculescu, Circularand semi-circular systems and free productfactors, Operator alge- bras, Unitary representations, envelopping algebras, and invariant theory, Progress
  • [17] D. Voiculescu, Limit laws for random matrices andfree 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.
  • [4] PLACE JUSSIEU, 75252, PARIS CEDEX 05