Sur la loi de Polya régissant les faits corrélatifs. II
Symmetric partitions and pairings
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.
Symmetrization of Bernoulli.
Symmetrization of probability measures, pushforward of order 2 and the Boolean convolution
We study relations between the Boolean convolution and the symmetrization and the pushforward of order 2. In particular we prove that if μ₁,μ₂ are probability measures on [0,∞) then and if ν₁,ν₂ are symmetric then . Finally we investigate necessary and sufficient conditions under which the latter equality holds.
The Barnes G function and its relations with sums and products of generalized gamma convolution variables.
The connection between the proximate order of an entire characteristic function and the corresponding distribution function
The inverse distribution for a dichotomous random variable
In this paper we will deal with the determination of the inverse of a dichotomous probability distribution. In particular it will be shown that a dichotomous distribution admit inverse if and only if it corresponds to a random variable assuming values , . Moreover we will provide two general results about the behaviour of the inverse distribution relative to the power and to a linear transformation of a measure.
The Laplace transform of measures on the cone of a vector lattice.
The Lévy-Khintchine formula and Nica-Speicher property for deformations of the free convolution
We study deformations of the free convolution arising via invertible transformations of probability measures on the real line T:μ ↦ Tμ. We define new associative convolutions of measures by . We discuss infinite divisibility with respect to these convolutions, and we establish a Lévy-Khintchine formula. We conclude the paper by proving that for any such deformation of free probability all probability measures μ have the Nica-Speicher property, that is, one can find their convolution power for...
The non-central g-distribution and its application
The -deformation of the classical convolution
We study deformations of the classical convolution. For every invertible transformation T:μ ↦ Tμ, we are able to define a new associative convolution of measures by . We deal with the -deformation of the classical convolution. We prove the analogue of the classical Lévy-Khintchine formula. We also show the central limit measure, which turns out to be the standard Gaussian measure. Moreover, we calculate the Poisson measure in the -deformed classical convolution and give the orthogonal polynomials...
Weak convergence of linear rank statistics
What are cumulants?
Zeros of smallest modulus of functions resembling exp(z).
Аналитическое уточнение теоремы Хайде о линейных формах от независимых случайных величин
Квази-вероятностные плотности Вигнера и характеризация гауссовского распределения
Классы комплекснозначных борелевских мер, в которых имеет место однозначная определённость сужениями
Некоторые оценки близости распределений в терминах характеристических функций
О восстановлении распределения по средним значениям минимумов случайного числа случайных величин
О поведении почти наверное случайной последовательности