Notions of independence related to the free group

Luigi Accardi, Yukihiro Hashimoto, Nobuaki Obata

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)201-220
Number of pages20
JournalInfinite Dimensional Analysis, Quantum Probability and Related Topics
Issue number2
Publication statusPublished - 1998 Apr


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