# Singleton independence

Luigi Accardi; Yukihiro Hashimoto; Nobuaki Obata

Banach Center Publications (1998)

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

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topAccardi, 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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