Singleton independence

Luigi Accardi; Yukihiro Hashimoto; Nobuaki Obata

Banach Center Publications (1998)

  • Volume: 43, Issue: 1, page 9-24
  • ISSN: 0137-6934

Abstract

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Motivated by the central limit problem for algebraic probability spaces arising from the Haagerup states on the free group with countably infinite generators, we introduce a new notion of statistical independence in terms of inequalities rather than of usual algebraic identities. In the case of the Haagerup states the role of the Gaussian law is played by the Ullman distribution. The limit process is realized explicitly on the finite temperature Boltzmannian Fock space. Furthermore, a functional central limit theorem associated with the Haagerup states is proved and the limit white noise is investigated.

How to cite

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Accardi, Luigi, Hashimoto, Yukihiro, and Obata, Nobuaki. "Singleton independence." Banach Center Publications 43.1 (1998): 9-24. <http://eudml.org/doc/208869>.

@article{Accardi1998,
abstract = {Motivated by the central limit problem for algebraic probability spaces arising from the Haagerup states on the free group with countably infinite generators, we introduce a new notion of statistical independence in terms of inequalities rather than of usual algebraic identities. In the case of the Haagerup states the role of the Gaussian law is played by the Ullman distribution. The limit process is realized explicitly on the finite temperature Boltzmannian Fock space. Furthermore, a functional central limit theorem associated with the Haagerup states is proved and the limit white noise is investigated.},
author = {Accardi, Luigi, Hashimoto, Yukihiro, Obata, Nobuaki},
journal = {Banach Center Publications},
keywords = {Ullman distribution; Boltzmannian Fock space; functional central limit theorem; Haagerup states},
language = {eng},
number = {1},
pages = {9-24},
title = {Singleton independence},
url = {http://eudml.org/doc/208869},
volume = {43},
year = {1998},
}

TY - JOUR
AU - Accardi, Luigi
AU - Hashimoto, Yukihiro
AU - Obata, Nobuaki
TI - Singleton independence
JO - Banach Center Publications
PY - 1998
VL - 43
IS - 1
SP - 9
EP - 24
AB - Motivated by the central limit problem for algebraic probability spaces arising from the Haagerup states on the free group with countably infinite generators, we introduce a new notion of statistical independence in terms of inequalities rather than of usual algebraic identities. In the case of the Haagerup states the role of the Gaussian law is played by the Ullman distribution. The limit process is realized explicitly on the finite temperature Boltzmannian Fock space. Furthermore, a functional central limit theorem associated with the Haagerup states is proved and the limit white noise is investigated.
LA - eng
KW - Ullman distribution; Boltzmannian Fock space; functional central limit theorem; Haagerup states
UR - http://eudml.org/doc/208869
ER -

References

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