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On averages of randomized class functions on the symmetric groups and their asymptotics

Paul-Olivier Dehaye, Dirk Zeindler (2013)

Annales de l’institut Fourier

The second author had previously obtained explicit generating functions for moments of characteristic polynomials of permutation matrices ( n points). In this paper, we generalize many aspects of this situation. We introduce random shifts of the eigenvalues of the permutation matrices, in two different ways: independently or not for each subset of eigenvalues associated to the same cycle. We also consider vastly more general functions than the characteristic polynomial of a permutation matrix, by...

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

Marcin Marciniak (1998)

Studia Mathematica

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.

On the connection between cherry-tree copulas and truncated R-vine copulas

Edith Kovács, Tamás Szántai (2017)

Kybernetika

Vine copulas are a flexible way for modeling dependences using only pair-copulas as building blocks. However if the number of variables grows the problem gets fastly intractable. For dealing with this problem Brechmann at al. proposed the truncated R-vine copulas. The truncated R-vine copula has the very useful property that it can be constructed by using only pair-copulas and a lower number of conditional pair-copulas. In our earlier papers we introduced the concept of cherry-tree copulas. In this...

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