منابع مشابه
Cumulants, free cumulants and half-shuffles.
Free cumulants were introduced as the proper analogue of classical cumulants in the theory of free probability. There is a mix of similarities and differences, when one considers the two families of cumulants. Whereas the combinatorics of classical cumulants is well expressed in terms of set partitions, that of free cumulants is described and often introduced in terms of non-crossing set partit...
متن کاملWhat are cumulants?
Abstra t. Let P be the set of all probability measures on R possessing moments of every order. Consider P as a semigroup with respe t to onvolution. After topologizing P in a natural way, we determine all ontinuous homomorphisms of P into the unit ir le and, as a orollary, those into the real line. The latter are pre isely the nite linear ombinations of umulants, and from these all the former a...
متن کاملThe Monotone Cumulants
In the present paper we define the notion of generalized cumulants which gives a universal framework for commutative, free, Boolean, and especially, monotone probability theories. The uniqueness of generalized cumulants holds for each independence, and hence, generalized cumulants are equal to the usual cumulants in commutative, free and Boolean cases. The way we define (generalized) cumulants ...
متن کاملCombinatorics of Free Cumulants
We derive a formula for expressing free cumulants whose entries are products of random variables in terms of the lattice structure of non-crossing partitions. We show the usefulness of that result by giving direct and conceptually simple proofs for a lot of results about R-diagonal elements. Our investigations do not assume the trace property for the considered linear functionals. Introduction ...
متن کاملJack polynomials and free cumulants
We study the coefficients in the expansion of Jack polynomials in terms of power sums. We express them as polynomials in the free cumulants of the transition measure of an anisotropic Young diagram. We conjecture that such polynomials have nonnegative integer coefficients. This extends recent results about normalized characters of the symmetric group. 2000 Mathematics Subject Classification: 05...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2000
ISSN: 0196-8858
DOI: 10.1006/aama.2000.0692