Results 141 to 150 of about 3,383,288 (169)

Free Cumulants and Enumeration of Connected Partitions

European Journal of Combinatorics, 2002
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 classical distributions, notably Gaussian and Poisson distributions. The latter count connected pairings and connected set partitions respectively.
Franz Lehner
exaly   +6 more sources

Combinatorics of Free Cumulants [PDF]

Journal of Combinatorial Theory - Series A, 2000
26 pages ...
Roland Speicher
exaly   +5 more sources

On the computation of classical, boolean and free cumulants [PDF]

Applied Mathematics and Computation, 2009
This paper introduces a simple and computationally efficient algorithm for conversion formulae between moments and cumulants. The algorithm provides just one formula for classical, boolean and free cumulants. This is realized by using a suitable polynomial representation of Abel polynomials.
Elvira di Nardo
exaly   +7 more sources

Jack polynomials and free cumulants [PDF]

Advances in Mathematics, 2009
43 pages, LaTeX, to appear in Adv ...
Michel Lassalle
exaly   +5 more sources

Star-cumulants of free unitary Brownian motion

Advances in Applied Mathematics, 2015
35 pages.
Alexandru Nica, Mathieu Guay-Paquet
exaly   +8 more sources

Boolean, free, and classical cumulants as tree enumerations [PDF]

Advances in Applied Mathematics
Defant found that the relationship between a sequence of (univariate) classical cumulants and the corresponding sequence of (univariate) free cumulants can be described combinatorially in terms of families of binary plane trees called troupes. Using a generalization of troupes that we call weighted troupes, we generalize this result to allow for ...
Colin Defant
exaly   +5 more sources

Cumulants for finite free convolution [PDF]

Journal of Combinatorial Theory - Series A, 2018
In this paper we define cumulants for finite free convolution. We give a moment-cumulant formula and show that these cumulants satisfy desired properties: they are additive with respect to finite free convolution and they approach free cumulants as the dimension goes to infinity.
Octavio Arizmendi
exaly   +4 more sources

Free cumulants, Schröder trees, and operads

Advances in Applied Mathematics, 2017
23 ...
Jean-Yves Thibon, Jean-Christophe Novelli   +1 more
exaly   +3 more sources

Zonal polynomials via Stanleyʼs coordinates and free cumulants

Journal of Algebra, 2011
45 pages, second version, important ...
Piotr Śniady, Valentin Feray
exaly   +4 more sources

Monotone, free, and boolean cumulants: A shuffle algebra approach [PDF]

Advances in Mathematics, 2018
final ...
Kurusch Ebrahimi-Fard, Frédéric Patras   +1 more
exaly   +4 more sources