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math.CO2002★ 44 cited
Cumulants in noncommutative probability II. Generalized Gaussian random variables
Franz Lehner
We continue the investigation of noncommutative cumulants. In this paper various characterizations of noncommutative Gaussian random variables are proved.
math.CO2001
Free cumulants and enumeration of connected partitions
Franz Lehner
A combinatorial formula is derived which expresses free cumulants in terms of classical comulants. As a corollary, we give a combinatorial interpretation of free cumulants of class…
math.CO2001
Cumulants, lattice paths, and orthogonal polynomials
Franz Lehner
A formula expressing free cumulants in terms of the Jacobi parameters of the corresponding orthogonal polynomials is derived. It combines Flajolet's theory of continued fractions a…