### Abstract

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 language | English |
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Pages (from-to) | 201-220 |

Number of pages | 20 |

Journal | Infinite Dimensional Analysis, Quantum Probability and Related Topics |

Volume | 1 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1998 Apr |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Mathematical Physics
- Applied Mathematics

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## Cite this

*Infinite Dimensional Analysis, Quantum Probability and Related Topics*,

*1*(2), 201-220. https://doi.org/10.1142/S0219025798000132