A noncommutative limit theorem for homogeneous correlations

• Autorzy: Romuald Lenczewski
• Języki publikacji: EN

Abstrakty

EN

We state and prove a noncommutative limit theorem for correlations which are homogeneous with respect to order-preserving injections. The most interesting examples of central limit theorems in quantum probability (for commuting, anticommuting, and free independence and also various q-qclt's), as well as the limit theorems for the Poisson law and the free Poisson law are special cases of the theorem. In particular, the theorem contains the q-central limit theorem for non-identically distributed variables, derived in our previous work in the context of q-bialgebras and quantum groups. More importantly, new examples of limit theorems of q-Poisson type are derived for both the infinite tensor product algebra and the reduced free product, leading to new q-laws. In the first case the limit as q → 1 is studied in more detail and a connection with partial Bell polynomials is established.

Kategorie tematyczne

• 60F05: Central limit and other weak theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 129
• Numer: 3
• Strony: 225-252

Daty

wydano

1998

otrzymano

1997-02-10

poprawiono

1997-11-06

Twórcy

autor

Romuald Lenczewski

• Hugo Steinhaus Center for Stochastic Methods, Institute of Mathematics, Technical University of Wrocław, 50-370 Wrocław, Poland

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