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Multivariate generalized Gamma convolutions are distributions defined by a convolutional semi-parametric structure. Their flexible dependence structures, the marginal possibilities and their useful convolutional expression make them…
The solutions to many problems in the mathematical, computational, and physical sciences often involve multidimensional integrals. A direct numerical evaluation of the integral incurs a computational cost that is exponential in the number…
We give a precise functional comparison between classical and free convolutions. If $\mu$ and $\nu$ are compactly supported probability measures, we show that the expectation of $f$ over the classical convolution $\mu * \nu$ is at least the…
In this paper, we analyse a method for approximating the distribution function and density of a random variable that depends in a non-trivial way on a possibly high number of independent random variables, each with support on the whole real…
Estimating the marginal and joint densities of the long-term average intakes of different dietary components is an important problem in nutritional epidemiology. Since these variables cannot be directly measured, data are usually collected…
Compensated convex transforms have been introduced for extended real-valued functions defined over $\mathbb{R}^n$. In their application to image processing, interpolation, and shape interrogation, where one deals with functions defined over…
Magneto-acousto-electrical tomography (MAET), a combination of ultrasound imaging and electrical impedance tomography (EIT), offers both high resolution (in comparison to EIT) and high contrast (in comparison to ultrasound imaging). It is…
Copulas allow a flexible and simultaneous modeling of complicated dependence structures together with various marginal distributions. Especially if the density function can be represented as the product of the marginal density functions and…
Vertex direction algorithms have been around for a few decades in the experimental design and mixture models literature. We briefly review this type of algorithm and describe a new member of the family: the support reduction algorithm. The…
The equivalence of the characteristic function approach and the probabilistic approach to monotone and boolean convolutions is proven for non-compactly supported probability measures. A probabilistically motivated definition of the…
It is a classical result in complex analysis that the class of functions that arise as the Cauchy transform of probability measures may be characterized entirely in terms of their analytic and asymptotic properties. Such transforms are a…
We define the rectangular additive convolution of polynomials with nonnegative real roots as a generalization of the asymmetric additive convolution introduced by Marcus, Spielman and Srivastava. We then prove a sliding bound on the largest…
This paper deals with characterizing the freeness and asymptotic freeness of free multiple integrals with respect to a free Brownian motion or a free Poisson process. We obtain three characterizations of freeness, in terms of contraction…
Based on the~method of subordinating functions we prove bounds for the minimal error of approximations of $n$-fold convolutions of probability measures by free infinitely divisible probability measures.
We study the "Fourier symmetry" of measures and distributions on the circle, in relation with the size of their supports. The main results of this paper are: (1) A one-side extension of Frostman's theorem, which connects the rate of decay…
We propose a method for computing numerically integrals defined via $i \epsilon$ deformations acting on single-pole singularities. We achieve this without an explicit analytic contour deformation. Our solution is then used to produce…
We survey general properties of multiplicative arithmetic functions of several variables and related convolutions, including the Dirichlet convolution and the unitary convolution. We introduce and investigate a new convolution, called gcd…
Macdonald processes are measures on sequences of integer partitions built using the Cauchy summation identity for Macdonald symmetric functions. These measures are a useful tool to uncover the integrability of many probabilistic systems,…
We compute exactly the mean perimeter <L(T)> and the mean area <A(T)> of the convex hull of a random acceleration process of duration T in two dimensions. We use an exact mapping that relates, via Cauchy's formulae, the computation of the…
We describe a method to evaluate integrals that arise in the asymptotic analysis when two saddle points may be close together. These integrals, which appear in problems from optics, acoustics or quantum mechanics as well as in a wide class…