no. 3
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 
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     title = {Martin boundary theory of some quantum random walks},
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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

[1] L. Accardi, A. Frigerio, J.T. Lewis, Quantum stochastic processes, Publ. Res. Inst. Math. Sci. 18 (1) (1982) 97-133. | Zbl | MR

[2] S. Baaj, G. Skandalis, Unitaires multiplicatifs et dualité pour les produits croisés de C∗-algèbres, Ann. Sci. École Norm. Sup. (4) 26 (4) (1993) 425-488. | Zbl | Numdam

[3] P. Biane, R. Durrett, Lectures on probability theory, in: Bernard P. (Ed.), Lectures from the Twenty-third Saint-Flour Summer School held August 18-September 4, 1993 , Springer-Verlag, Berlin, 1995. | Zbl

[4] Ph. Biane, Équation de Choquet-Deny sur le dual d'un groupe compact, Probab. Theory Related Fields 94 (1) (1992) 39-51. | Zbl

[5] P. Biane, Marches de Bernoulli quantiques, in: Séminaire de Probabilités, XXIV, 1988/89, Springer, Berlin, 1990, pp. 329-344. | Zbl | MR | Numdam

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

[7] P. Biane, Some properties of quantum Bernoulli random walks, in: Quantum Probability & Related Topics, World Scientific, River Edge, NJ, 1991, pp. 193-203. | Zbl | MR

[8] P. Biane, Minuscule weights and random walks on lattices, in: Quantum Probability & Related Topics, World Scientific, River Edge, NJ, 1992, pp. 51-65. | Zbl | MR

[9] P. Biane, Théorème de Ney-Spitzer sur le dual de su(2), Trans. Amer. Math. Soc. 345 (1) (1994) 179-194. | Zbl

[10] G. Choquet, J. Deny, Sur l'équation de convolution μ=μ∗σ, C. R. Acad. Sci. Paris 250 (1960) 799-801. | Zbl

[11] J. Dixmier, Les C∗-algèbres et leurs représentations, Gauthier-Villars & Cie, Paris, 1964. | Zbl

[12] E.G. Effros, Z.-J. Ruan, Discrete quantum groups. I. The Haar measure, Internat. J. Math. 5 (5) (1994) 681-723. | Zbl | MR

[13] W. Fulton, Young tableaux, Cambridge University Press, Cambridge, 1997, With applications to representation theory and geometry. | Zbl | MR

[14] W. Fulton, J. Harris, Representation Theory, Springer-Verlag, New York, 1991, A first course, Readings in Mathematics. | Zbl | MR

[15] F. Hiai, M. Izumi, Amenability and strong amenability for fusion algebras with applications to subfactor theory, Internat. J. Math. 9 (6) (1998) 669-722. | Zbl | MR

[16] M. Izumi, Actions of compact quantum groups on operator algebras, Sūrikaisekikenkyūsho Kōkyūroku 1024 (1998) 55-60, Profound development of operator algebras (Japanese) (Kyoto, 1997). | Zbl | MR

[17] M. Izumi, 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] M. Izumi, Non-commutative Poisson boundaries and compact quantum group actions, Adv. Math. 169 (1) (2002) 1-57. | Zbl | MR

[19] M. Izumi, Non-commutative Poisson boundaries and compact quantum group actions, November 29, 2000.

[20] J.G. Kemeny, J.L. Snell, A.W. Knapp, Denumerable Markov Chains, Graduate Texts in Mathematics, vol. 40, Springer-Verlag, New York, 1976, With a chapter on Markov random fields, by D. Griffeath. | Zbl | MR

[21] P.-A. Meyer, Éléments de probabilités quantiques. I-V, in: Séminaire de Probabilités, XX, 1984/85 , Springer, Berlin, 1986, pp. 186-312. | Zbl | Numdam

[22] P.-A. Meyer, Éléments de probabilités quantiques. VI-VIII, in: Séminaire de Probabilités, XXI, Springer, Berlin, 1987, pp. 33-78. | Zbl | Numdam

[23] P.-A. Meyer, Eléments de probabilités quantiques. IX. Calculs antisymétriques et “supersymétriques” en probabilités, in: Séminaire de Probabilités, XXII, Springer, Berlin, 1988, pp. 101-123. | Zbl | Numdam

[24] P.-A. Meyer, Éléments de probabilités quantiques. X. Calculs avec des noyaux discrets, in: Séminaire de Probabilités, XXII, Springer, Berlin, 1988, pp. 124-128. | Zbl | MR | Numdam

[25] P.-A. Meyer, 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. | Zbl | MR | Numdam

[26] P.-A. Meyer, 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. | Zbl | MR | Numdam

[27] S. Neshveyev, L. Tuset, The Martin boundary of a discrete quantum group, 2002.

[28] P. Ney, F. Spitzer, The Martin boundary for random walk, Trans. Amer. Math. Soc. 121 (1966) 116-132. | Zbl | MR

[29] D. Revuz, Markov Chains, North-Holland, Amsterdam, 1984. | Zbl | MR

[30] M. Schürmann, M. Skeide, Infinitesimal generators on the quantum group suq(2), Infin. Dimens. Anal. Quantum Probab. Relat. Top. 1 (4) (1998) 573-598. | Zbl | MR

[31] D.V. Voiculescu, K.J. Dykema, A. Nica, 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. | Zbl | MR

[32] S.L. Woronowicz, Compact matrix pseudogroups, Comm. Math. Phys. 111 (4) (1987) 613-665. | Zbl | MR

[33] S.L. Woronowicz, Tannaka-Kreĭn duality for compact matrix pseudogroups. Twisted su(N) groups, Invent. Math. 93 (1) (1988) 35-76. | Zbl

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