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.
@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://www.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://www.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://www.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://www.numdam.org/articles/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. | MR | Zbl

[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. | Numdam | Zbl

[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. | Numdam | MR | Zbl

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

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

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

[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. | MR | Zbl

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

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

[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. | MR | Zbl

[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). | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

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

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

[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. | Numdam | Zbl

[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. | Numdam | MR | Zbl

[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. | Numdam | MR | Zbl

[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. | Numdam | MR | Zbl

[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. | MR | Zbl

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

[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. | MR | Zbl

[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. | MR | Zbl

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

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

Cité par Sources :