Notions of independence related to the free group

Luigi Accardi, Yukihiro Hashimoto, Nobuaki Obata

研究成果: Article査読

28 被引用数 (Scopus)

抄録

The central limit problem for algebraic probability spaces associated with the Haagerup states on the free group with countably many generators leads to a new form of statistical independence in which the singleton condition is not satisfied. This circumstance allows us to obtain nonsymmetric distributions from the central limit theorems deduced from this notion of independence. In the particular case of the Haagerup states, the role of the Gauasian law is played by the Ullman distribution. The limit process is explicitly realized on the finite temperature Boltzmannian Fock space. The role of entangled ergodic theorems in the proof of the central limit theorems is discussed.

本文言語English
ページ(範囲)201-220
ページ数20
ジャーナルInfinite Dimensional Analysis, Quantum Probability and Related Topics
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2
DOI
出版ステータスPublished - 1998 4月
外部発表はい

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 統計学および確率
  • 数理物理学
  • 応用数学

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