A Constructive Boolean Central Limit Theorem
Ben Ghorbal, Anis ; Crismale, Vitonofrio ; Lu, Yun Gang
Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007), p. 593-604 / Harvested from Biblioteca Digitale Italiana di Matematica

We give a construction of the creation, annihilation and number processes on the Boolean Fock space by means of a quantum central limit theorem starting from creation, annihilation and number processes with discrete time.

Si fornisce una costruzione dei processi di creazione, distruzione e numero sullo spazio di Fock Booleano a mezzo di un teorema di limite centrale quantistico partendo da processi di creazione, distruzione e numero con tempo discreto.

Publié le : 2007-10-01
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     author = {Anis Ben Ghorbal and Vitonofrio Crismale and Yun Gang Lu},
     title = {A Constructive Boolean Central Limit Theorem},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {10-A},
     year = {2007},
     pages = {593-604},
     zbl = {1139.60009},
     mrnumber = {2351531},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2007_8_10B_3_593_0}
}
Ben Ghorbal, Anis; Crismale, Vitonofrio; Lu, Yun Gang. A Constructive Boolean Central Limit Theorem. Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007) pp. 593-604. http://gdmltest.u-ga.fr/item/BUMI_2007_8_10B_3_593_0/

[1] Accardi, L. - Bach, A., The harmonic oscillator as quantum central limit theorem for monotone noise, preprint (1985). | Zbl 0553.60031

[2] Accardi, L. - Ben Ghorbal, A. - Crismale, V. - Lu, Y. G., Projective independence and quantum central limit theorem, preprint (2007). | MR 2351531

[3] Accardi, L. - Crismale, V. - Lu, Y. G., Constructive universal central limit theorems based on interacting Fock spaces, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 8, no. 4 (2005), 631-650. | MR 2184087 | Zbl 1079.60501

[4] Accardi, L. - Hashimoto, Y. - Obata, N., Notions of independence related to the free group, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 1, no. 2 (1998), 201-220. | MR 1628248 | Zbl 0913.46057

[5] Ben Ghorbal, A. - Schürmann, M., Noncommutative notions of stochastic independence, Math. Proc. Cambridge Philos. Soc., 133, no. 3 (2002), 531-561. | MR 1919720 | Zbl 1028.46094

[6] Ben Ghorbal, A. - Schürmann, M., Quantum stochastic calculus on Boolean Fock Space, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 7, no. 4 (2004), 631-650. | MR 2105916 | Zbl 1077.81061

[7] Bozejko, M., Uniformly bounded representations of free groups, J. Reine Angew. Math., 377 (1987), 170-186. | MR 887407 | Zbl 0604.43004

[8] De Giosa, M. - Lu, Y. G., The free creation and annihilation operators as the central limit of the quantum Bernoulli process, Random Oper. Stoch. Eq. 5, no. 3 (1997), 227- 236. | MR 1483010 | Zbl 0927.60066

[9] Lenczewski, R., Stochastic calculus on multiple symmetric Fock spaces, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 4, no. 2 (2001), 309-346. | MR 1852853 | Zbl 1042.81052

[10] Liebsher, V., On a central limit theorem for monotone noise, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 2, no. 2 (1999), 155-167. | MR 1805839

[11] Lu, Y. G., The Boson and Fermion quantum Brownian motions as quantum central limits of the quantum Bernoulli processes, Boll. Un. Mat. Ital. B (7) 6, no. 2 (1992), 245-273. | MR 1171102 | Zbl 0858.60026

[12] Meyer, P. A., "Quantum probability for probabilists", Lecture Notes in Mathematics1538, Springer-Verlag, Berlin, 1993. | MR 1222649 | Zbl 0773.60098

[13] Muraki, N., The five independencies as natural products, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 6, no. 3 (2003), 337-371. | MR 2016316 | Zbl 1053.81057

[14] Skeide, M., Quantum stochastic calculus on full Fock modules, J. Funct. Anal., 173, no. 2 (2000), 401-452. | MR 1760621 | Zbl 0973.46057

[15] Speicher, R., On universal product, Fields Inst. Commun., 12 (1997), 257-266. | MR 1426844 | Zbl 0877.46044

[16] Speicher, R. - Von Waldenfels, W., A general central limit theorem and invariance principle, in Quantum Probability and Related Topics, Editor L. Accardi, World Scientific Vol., 9 (1994), 371-387.

[17] Speicher, R. - Woroudi, R., Boolean convolution, Fields Inst. Commun., 12 (1997), 267-279. | MR 1426845

[18] Von Waldenfels, W., An approach to the theory of pressure broadening of spectral lines, In: "Probability and Information Theory II", M. Behara - K. Krickeberg - J. Wolfowitz (eds.), Lect. Notes Math., 296 (1973), 19-64. | MR 421496