@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}, pages = {367--384}, publisher = {Elsevier}, volume = {40}, number = {3}, year = {2004}, doi = {10.1016/j.anihpb.2003.10.004}, mrnumber = {2060458}, zbl = {1051.31005}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpb.2003.10.004/} }
TY - JOUR AU - Collins, Benoît TI - Martin boundary theory of some quantum random walks JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2004 SP - 367 EP - 384 VL - 40 IS - 3 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpb.2003.10.004/ DO - 10.1016/j.anihpb.2003.10.004 LA - en ID - AIHPB_2004__40_3_367_0 ER -
%0 Journal Article %A Collins, Benoît %T Martin boundary theory of some quantum random walks %J Annales de l'I.H.P. Probabilités et statistiques %D 2004 %P 367-384 %V 40 %N 3 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpb.2003.10.004/ %R 10.1016/j.anihpb.2003.10.004 %G en %F 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) no. 3, pp. 367-384. doi : 10.1016/j.anihpb.2003.10.004. http://archive.numdam.org/articles/10.1016/j.anihpb.2003.10.004/
[1] Quantum stochastic processes, Publ. Res. Inst. Math. Sci. 18 (1) (1982) 97-133. | MR | Zbl
, , ,[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
, ,[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
, ,[4] Équation de Choquet-Deny sur le dual d'un groupe compact, Probab. Theory Related Fields 94 (1) (1992) 39-51. | Zbl
,[5] Marches de Bernoulli quantiques, in: Séminaire de Probabilités, XXIV, 1988/89, Springer, Berlin, 1990, pp. 329-344. | Numdam | MR | Zbl
,[6] Quantum random walk on the dual of su(n), Probab. Theory Related Fields 89 (1) (1991) 117-129. | MR | Zbl
,[7] Some properties of quantum Bernoulli random walks, in: Quantum Probability & Related Topics, World Scientific, River Edge, NJ, 1991, pp. 193-203. | MR | Zbl
,[8] Minuscule weights and random walks on lattices, in: Quantum Probability & Related Topics, World Scientific, River Edge, NJ, 1992, pp. 51-65. | MR | Zbl
,[9] Théorème de Ney-Spitzer sur le dual de su(2), Trans. Amer. Math. Soc. 345 (1) (1994) 179-194. | Zbl
,[10] Sur l'équation de convolution μ=μ∗σ, C. R. Acad. Sci. Paris 250 (1960) 799-801. | Zbl
, ,[11] Les C∗-algèbres et leurs représentations, Gauthier-Villars & Cie, Paris, 1964. | Zbl
,[12] Discrete quantum groups. I. The Haar measure, Internat. J. Math. 5 (5) (1994) 681-723. | MR | Zbl
, ,[13] Young tableaux, Cambridge University Press, Cambridge, 1997, With applications to representation theory and geometry. | MR | Zbl
,[14] Representation Theory, Springer-Verlag, New York, 1991, A first course, Readings in Mathematics. | MR | Zbl
, ,[15] Amenability and strong amenability for fusion algebras with applications to subfactor theory, Internat. J. Math. 9 (6) (1998) 669-722. | MR | Zbl
, ,[16] Actions of compact quantum groups on operator algebras, Sūrikaisekikenkyūsho Kōkyūroku 1024 (1998) 55-60, Profound development of operator algebras (Japanese) (Kyoto, 1997). | MR | Zbl
,[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
,[18] Non-commutative Poisson boundaries and compact quantum group actions, Adv. Math. 169 (1) (2002) 1-57. | MR | Zbl
,[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 | Zbl
, , ,[21] Éléments de probabilités quantiques. I-V, in: Séminaire de Probabilités, XX, 1984/85 , Springer, Berlin, 1986, pp. 186-312. | Numdam | Zbl
,[22] Éléments de probabilités quantiques. VI-VIII, in: Séminaire de Probabilités, XXI, Springer, Berlin, 1987, pp. 33-78. | Numdam | Zbl
,[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
,[24] Éléments de probabilités quantiques. X. Calculs avec des noyaux discrets, in: Séminaire de Probabilités, XXII, Springer, Berlin, 1988, pp. 124-128. | Numdam | MR | Zbl
,[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 | Zbl
,[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 | Zbl
,[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 | Zbl
, ,[29] Markov Chains, North-Holland, Amsterdam, 1984. | MR | Zbl
,[30] Infinitesimal generators on the quantum group suq(2), Infin. Dimens. Anal. Quantum Probab. Relat. Top. 1 (4) (1998) 573-598. | MR | Zbl
, ,[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 | Zbl
, , ,[32] Compact matrix pseudogroups, Comm. Math. Phys. 111 (4) (1987) 613-665. | MR | Zbl
,[33] Tannaka-Kreĭn duality for compact matrix pseudogroups. Twisted su(N) groups, Invent. Math. 93 (1) (1988) 35-76. | Zbl
,Cité par Sources :