@article{AIHPB_2004__40_3_367_0, author = {Collins, Beno\^\i t}, title = {Martin boundary theory of some quantum random walks}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, volume = {40}, year = {2004}, pages = {367-384}, doi = {10.1016/j.anihpb.2003.10.004}, mrnumber = {2060458}, zbl = {1051.31005}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPB_2004__40_3_367_0} }
Collins, Benoît. Martin boundary theory of some quantum random walks. Annales de l'I.H.P. Probabilités et statistiques, Tome 40 (2004) pp. 367-384. doi : 10.1016/j.anihpb.2003.10.004. http://gdmltest.u-ga.fr/item/AIHPB_2004__40_3_367_0/
[1] Quantum stochastic processes, Publ. Res. Inst. Math. Sci. 18 (1) (1982) 97-133. | MR 660823 | Zbl 0498.60099
, , ,[2] Unitaires multiplicatifs et dualité pour les produits croisés de C∗-algèbres, Ann. Sci. École Norm. Sup. (4) 26 (4) (1993) 425-488. | Numdam | Zbl 0804.46078
, ,[3] Lectures on probability theory, in: (Ed.), Lectures from the Twenty-third Saint-Flour Summer School held August 18-September 4, 1993 , Springer-Verlag, Berlin, 1995. | Zbl 0822.00009
, ,[4] Équation de Choquet-Deny sur le dual d'un groupe compact, Probab. Theory Related Fields 94 (1) (1992) 39-51. | Zbl 0766.46044
,[5] Marches de Bernoulli quantiques, in: Séminaire de Probabilités, XXIV, 1988/89, Springer, Berlin, 1990, pp. 329-344. | Numdam | MR 1071548 | Zbl 0701.60103
,[6] Quantum random walk on the dual of su(n), Probab. Theory Related Fields 89 (1) (1991) 117-129. | MR 1109477 | Zbl 0746.46058
,[7] Some properties of quantum Bernoulli random walks, in: Quantum Probability & Related Topics, World Scientific, River Edge, NJ, 1991, pp. 193-203. | MR 1149826 | Zbl 0945.81505
,[8] Minuscule weights and random walks on lattices, in: Quantum Probability & Related Topics, World Scientific, River Edge, NJ, 1992, pp. 51-65. | MR 1186654 | Zbl 0787.60089
,[9] Théorème de Ney-Spitzer sur le dual de su(2), Trans. Amer. Math. Soc. 345 (1) (1994) 179-194. | Zbl 0814.60064
,[10] Sur l'équation de convolution μ=μ∗σ, C. R. Acad. Sci. Paris 250 (1960) 799-801. | Zbl 0093.12802
, ,[11] Les C∗-algèbres et leurs représentations, Gauthier-Villars & Cie, Paris, 1964. | Zbl 0152.32902
,[12] Discrete quantum groups. I. The Haar measure, Internat. J. Math. 5 (5) (1994) 681-723. | MR 1297413 | Zbl 0824.17020
, ,[13] Young tableaux, Cambridge University Press, Cambridge, 1997, With applications to representation theory and geometry. | MR 1464693 | Zbl 0878.14034
,[14] Representation Theory, Springer-Verlag, New York, 1991, A first course, Readings in Mathematics. | MR 1153249 | Zbl 0744.22001
, ,[15] Amenability and strong amenability for fusion algebras with applications to subfactor theory, Internat. J. Math. 9 (6) (1998) 669-722. | MR 1644299 | Zbl 0978.46043
, ,[16] Actions of compact quantum groups on operator algebras, Sūrikaisekikenkyūsho Kōkyūroku 1024 (1998) 55-60, Profound development of operator algebras (Japanese) (Kyoto, 1997). | MR 1643711 | Zbl 0960.58004
,[17] Actions of compact quantum groups on operator algebras, in: XIIth International Congress of Mathematical Physics (ICMP '97) (Brisbane) , Internat. Press, Cambridge, MA, 1999, pp. 249-253. | MR 1697285
,[18] Non-commutative Poisson boundaries and compact quantum group actions, Adv. Math. 169 (1) (2002) 1-57. | MR 1916370 | Zbl 1037.46056
,[19] M. Izumi, Non-commutative Poisson boundaries and compact quantum group actions, November 29, 2000.
[20] Denumerable Markov Chains, Graduate Texts in Mathematics, vol. 40, Springer-Verlag, New York, 1976, With a chapter on Markov random fields, by D. Griffeath. | MR 407981 | Zbl 0348.60090
, , ,[21] Éléments de probabilités quantiques. I-V, in: Séminaire de Probabilités, XX, 1984/85 , Springer, Berlin, 1986, pp. 186-312. | Numdam | Zbl 0604.60001
,[22] Éléments de probabilités quantiques. VI-VIII, in: Séminaire de Probabilités, XXI, Springer, Berlin, 1987, pp. 33-78. | Numdam | Zbl 0633.60074
,[23] Eléments de probabilités quantiques. IX. Calculs antisymétriques et “supersymétriques” en probabilités, in: Séminaire de Probabilités, XXII, Springer, Berlin, 1988, pp. 101-123. | Numdam | Zbl 0659.60077
,[24] Éléments de probabilités quantiques. X. Calculs avec des noyaux discrets, in: Séminaire de Probabilités, XXII, Springer, Berlin, 1988, pp. 124-128. | Numdam | MR 960516 | Zbl 0659.60077
,[25] Éléments de probabilités quantiques. X [bis]. Approximation de l'oscillateur harmonique (d'après L. Accardi et A. Bach), in: Séminaire de Probabilités, XXIII, Springer, Berlin, 1989, pp. 175-182. | Numdam | MR 1022909 | Zbl 0747.60105
,[26] Éléments de probabilités quantiques. XI. Caractérisation des lois de Bernoulli quantiques d'après K.R. Parthasarathy, in: Séminaire de Probabilités, XXIII, Springer, Berlin, 1989, pp. 183-185. | Numdam | MR 1022910 | Zbl 0739.46050
,[27] The Martin boundary of a discrete quantum group, 2002.
, ,[28] The Martin boundary for random walk, Trans. Amer. Math. Soc. 121 (1966) 116-132. | MR 195151 | Zbl 0141.15601
, ,[29] Markov Chains, North-Holland, Amsterdam, 1984. | MR 758799 | Zbl 0539.60073
,[30] Infinitesimal generators on the quantum group suq(2), Infin. Dimens. Anal. Quantum Probab. Relat. Top. 1 (4) (1998) 573-598. | MR 1665276 | Zbl 0924.60090
, ,[31] Free Random Variables, American Mathematical Society, Providence, RI, 1992, A noncommutative probability approach to free products with applications to random matrices, operator algebras and harmonic analysis on free groups. | MR 1217253 | Zbl 0795.46049
, , ,[32] Compact matrix pseudogroups, Comm. Math. Phys. 111 (4) (1987) 613-665. | MR 901157 | Zbl 0627.58034
,[33] Tannaka-Kreĭn duality for compact matrix pseudogroups. Twisted su(N) groups, Invent. Math. 93 (1) (1988) 35-76. | Zbl 0664.58044
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