Limit theorems for the hierarchy of freeness
Franz, Uwe ; Lenczewski, Romuald
HAL, hal-00470217 / Harvested from HAL
Text on HAL
The central limit theorem, the invariance principle and the Poisson limit theorem for the hierarchy of freeness are studied. We show that for given natural m the limit laws can be expressed in terms of non-crossing partitions of depth smaller or equal to m. For the algebra of polynomials in one variable we solve the associated moment problems and find explicitly the discrete limit measures.
Publié le : 2001-03-06
Classification:  [MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA],  [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph],  [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] 
@article{hal-00470217,
     author = {Franz, Uwe and Lenczewski, Romuald},
     title = {Limit theorems for the hierarchy of freeness},
     journal = {HAL},
     volume = {2001},
     number = {0},
     year = {2001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00470217}
}

Franz, Uwe; Lenczewski, Romuald. Limit theorems for the hierarchy of freeness. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-00470217/