Displaying similar documents to “What are cumulants?”

Symmetric partitions and pairings

Ferenc Oravecz (2000)

Colloquium Mathematicae

Similarity:

The lattice of partitions and the sublattice of non-crossing partitions of a finite set are important objects in combinatorics. In this paper another sublattice of the partitions is investigated, which is formed by the symmetric partitions. The measure whose nth moment is given by the number of non-crossing symmetric partitions of n elements is determined explicitly to be the "symmetric" analogue of the free Poisson law.

The monotone cumulants

Takahiro Hasebe, Hayato Saigo (2011)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

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 the commutative, free and Boolean cases. The way we define (generalized) cumulants needs neither partition lattices nor generating functions and then will give a new viewpoint...

On Q-independence, limit theorems and q-Gaussian distribution

Marcin Marciniak (1998)

Studia Mathematica

Similarity:

We formulate the notion of Q-independence which generalizes the classical independence of random variables and free independence introduced by Voiculescu. Here Q stands for a family of polynomials indexed by tiny partitions of finite sets. The analogs of the central limit theorem and Poisson limit theorem are proved. Moreover, it is shown that in some special cases this kind of independence leads to the q-probability theory of Bożejko and Speicher.