A Constructive Boolean Central Limit Theorem
Anis Ben Ghorbal; Vitonofrio Crismale; Yun Gang Lu
Bollettino dell'Unione Matematica Italiana (2007)
- Volume: 10-B, Issue: 3, page 593-604
- ISSN: 0392-4041
Access Full Article
topAbstract
topHow to cite
topBen Ghorbal, Anis, Crismale, Vitonofrio, and Lu, Yun Gang. "A Constructive Boolean Central Limit Theorem." Bollettino dell'Unione Matematica Italiana 10-B.3 (2007): 593-604. <http://eudml.org/doc/290361>.
@article{BenGhorbal2007,
abstract = {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.},
author = {Ben Ghorbal, Anis, Crismale, Vitonofrio, Lu, Yun Gang},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {593-604},
publisher = {Unione Matematica Italiana},
title = {A Constructive Boolean Central Limit Theorem},
url = {http://eudml.org/doc/290361},
volume = {10-B},
year = {2007},
}
TY - JOUR
AU - Ben Ghorbal, Anis
AU - Crismale, Vitonofrio
AU - Lu, Yun Gang
TI - A Constructive Boolean Central Limit Theorem
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/10//
PB - Unione Matematica Italiana
VL - 10-B
IS - 3
SP - 593
EP - 604
AB - 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.
LA - eng
UR - http://eudml.org/doc/290361
ER -
References
top- ACCARDI, L. - BACH, A., The harmonic oscillator as quantum central limit theorem for monotone noise, preprint (1985). Zbl0553.60031
- ACCARDI, L. - BEN GHORBAL, A. - CRISMALE, V. - LU, Y. G., Projective independence and quantum central limit theorem, preprint (2007). MR2351531
- 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. Zbl1079.60501MR2184087DOI10.1142/S021902570500213X
- 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. Zbl0913.46057MR1628248DOI10.1142/S0219025798000132
- BEN GHORBAL, A. - SCHÜRMANN, M., Noncommutative notions of stochastic independence, Math. Proc. Cambridge Philos. Soc., 133, no. 3 (2002), 531-561. Zbl1028.46094MR1919720DOI10.1017/S0305004102006072
- 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. Zbl1077.81061MR2105916DOI10.1142/S0219025704001815
- BOZEJKO, M., Uniformly bounded representations of free groups, J. Reine Angew. Math., 377 (1987), 170-186. Zbl0604.43004MR887407DOI10.1515/crll.1987.377.170
- 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. Zbl0927.60066MR1483010DOI10.1515/rose.1997.5.3.227
- LENCZEWSKI, R., Stochastic calculus on multiple symmetric Fock spaces, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 4, no. 2 (2001), 309-346. Zbl1042.81052MR1852853DOI10.1142/S0219025701000553
- LIEBSHER, V., On a central limit theorem for monotone noise, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 2, no. 2 (1999), 155-167. MR1805839DOI10.1142/S0219025799000084
- 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. Zbl0858.60026MR1171102
- MEYER, P. A., "Quantum probability for probabilists", Lecture Notes in Mathematics1538, Springer-Verlag, Berlin, 1993. Zbl0773.60098MR1222649DOI10.1007/978-3-662-21558-6
- MURAKI, N., The five independencies as natural products, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 6, no. 3 (2003), 337-371. Zbl1053.81057MR2016316DOI10.1142/S0219025703001365
- SKEIDE, M., Quantum stochastic calculus on full Fock modules, J. Funct. Anal., 173, no. 2 (2000), 401-452. Zbl0973.46057MR1760621DOI10.1006/jfan.2000.3579
- SPEICHER, R., On universal product, Fields Inst. Commun., 12 (1997), 257-266. Zbl0877.46044MR1426844
- 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.
- SPEICHER, R. - WOROUDI, R., Boolean convolution, Fields Inst. Commun., 12 (1997), 267-279. MR1426845
- 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. MR421496
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.