# A noncommutative limit theorem for homogeneous correlations

Studia Mathematica (1998)

- Volume: 129, Issue: 3, page 225-252
- ISSN: 0039-3223

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topLenczewski, Romuald. "A noncommutative limit theorem for homogeneous correlations." Studia Mathematica 129.3 (1998): 225-252. <http://eudml.org/doc/216502>.

@article{Lenczewski1998,

abstract = {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.},

author = {Lenczewski, Romuald},

journal = {Studia Mathematica},

keywords = {limit theorem; quantum probability; convergence of Poisson type},

language = {eng},

number = {3},

pages = {225-252},

title = {A noncommutative limit theorem for homogeneous correlations},

url = {http://eudml.org/doc/216502},

volume = {129},

year = {1998},

}

TY - JOUR

AU - Lenczewski, Romuald

TI - A noncommutative limit theorem for homogeneous correlations

JO - Studia Mathematica

PY - 1998

VL - 129

IS - 3

SP - 225

EP - 252

AB - 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.

LA - eng

KW - limit theorem; quantum probability; convergence of Poisson type

UR - http://eudml.org/doc/216502

ER -

## References

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