Ben Ghorbal, Crismale, Lu: A Constructive Boolean Central Limit Theorem

Ben Ghorbal, Anis and Crismale, Vitonofrio and Lu, Yun Gang:
A Constructive Boolean Central Limit Theorem
Bollettino dell'Unione Matematica Italiana Serie 8 10-B (2007), fasc. n.3, p. 593-604, Unione Matematica Italiana (English)
pdf (450 Kb), djvu (117 Kb). | MR 2351531 | Zbl 1139.60009

Sunto

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.

Referenze Bibliografiche

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

[2] L. ACCARDI - A. BEN GHORBAL - V. CRISMALE - Y. G. LU, Projective independence and quantum central limit theorem, preprint (2007). | MR 2351531

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

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

[5] A. BEN GHORBAL - M. SCHÜRMANN, Noncommutative notions of stochastic independence, Math. Proc. Cambridge Philos. Soc., 133, no. 3 (2002), 531-561. | fulltext (doi) | MR 1919720 | Zbl 1028.46094

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

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

[8] M. DE GIOSA - Y. G. LU, 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. | fulltext (doi) | MR 1483010 | Zbl 0927.60066

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

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

[11] Y. G. LU, 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] P. A. MEYER, "Quantum probability for probabilists", Lecture Notes in Mathematics 1538, Springer-Verlag, Berlin, 1993. | fulltext (doi) | MR 1222649 | Zbl 0773.60098

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

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

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

[16] R. SPEICHER - W. VON WALDENFELS, 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] R. SPEICHER - R. WOROUDI, Boolean convolution, Fields Inst. Commun., 12 (1997), 267-279. | MR 1426845

[18] W. VON WALDENFELS, 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

bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

Sunto

Referenze Bibliografiche