Geodesic
A noncommutative limit theorem for homogeneous correlations
Studia Mathematica, Tome 129 (1998) no. 3, pp. 225-252

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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.
DOI : 10.4064/sm-129-3-225-252

Romuald Lenczewski 1

1 
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Romuald Lenczewski. A noncommutative limit theorem for homogeneous correlations. Studia Mathematica, Tome 129 (1998) no. 3, pp. 225-252. doi: 10.4064/sm-129-3-225-252

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