Related papers: Boolean Cumulants and Subordination in Free Probab…
We define an extension of the polynomial calculus on a W*-probability space by introducing an abstract algebra which contains polynomials. This extension allows us to define transition operators for additive and multiplicative free…
We show that the distribution of the spectral maximum of monotonically independent self-adjoint operators coincides with the classical max-convolution of their distributions. In free probability, it was proven that for any probability…
We revisit the theory of operator-valued free convolution powers given by a completely positive map $\eta$. We first give a general result, with a new analytic proof, that the $\eta$-convolution power of the law of $X$ is realized by…
We discuss free probability theory and free harmonic analysis from a categorical perspective. In order to do so, we extend first the set of analytic convolutions and operations and then show that the comonadic structure governing free…
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…
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…
The paper presents several combinatorial properties of the boolean cumulants. A corollary is a new proof of the multiplicative property of the boolean cumulant series that can be easily adapted for the case of boolean independence with…
We extend to arbitrary measures results of Bao, Erd\"os, Schnelli, Moreillon, and Ji on the connectedness of the supports of additive convolutions of measures on \mathbb{R} and of free multiplicative convolutions of measures on…
This work investigates the combinatorial structures underlying cyclic conditional freeness and introduces cumulants that serve to linearize the cyclic conditional additive convolution. In the process, we establish the notion of "cyclic…
We define a new independence in non-commutative probability, called $\alpha$-freeness, with respect to a triplet of states. This concept unifies several independences in non-commutative probability, in particular, free, monotone,…
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…
We propose a new class of extreme-value copulas which are extreme-value limits of conditional normal models. Conditional normal models are generalizations of conditional independence models, where the dependence among observed variables is…
As a crucial problem in statistics is to decide whether additional variables are needed in a regression model. We propose a new multivariate test to investigate the conditional mean independence of Y given X conditioning on some known…
A system of nonlinear differential equations $x^{1+\gamma}\frac{dY}{dx}= F_0(x)+A(x)Y+F(x,Y)$ is considered. We study more precisely the meaning of asymptotic expansion of transformations and solutions than preceding pioneering works, by…
Several procedures have been recently proposed to test the simplifying assumption for conditional copulas. Instead of considering pointwise conditioning events, we study the constancy of the conditional dependence structure when some…
We consider general subordination and obtain the formula of the subordinated predictable compensator. An example of application is given.
We study the asymptotic behavior of the free cumulants (in the sense of free probability theory of Voiculescu) of Jucys--Murphy elements--or equivalently--of the transition measure associated with a Young diagram. We express these cumulants…
A Boolean function $g$ is said to be an optimal predictor for another Boolean function $f$, if it minimizes the probability that $f(X^{n})\neq g(Y^{n})$ among all functions, where $X^{n}$ is uniform over the Hamming cube and $Y^{n}$ is…
In this paper, we develop a unified regression approach to model unconditional quantiles, M-quantiles and expectiles of multivariate dependent variables exploiting the multidimensional Huber's function. To assess the impact of changes in…
We study the linear span of commutators of free random variables and show that these are the only quadratic forms which satisfy the following equivalent properties: * preservation free infinite divisibility * free and strong cancellation of…