相关论文: Cauchy-Stieltjes kernels families and free multipl…
We explore properties of Cauchy-Stieltjes families that have no counterpart in exponential families. We relate the variance function of the iterated Cauchy-Stieltjes family to the pseudo-variance function of the initial Cauchy-Stieltjes…
This paper continues the study of a kernel family which uses the Cauchy-Stieltjes kernel in place of the celebrated exponential kernel of the exponential families theory. We extend the theory to cover generating measures with support that…
This paper studies variance functions of Cauchy-Stieltjes Kernel families generated by compactly supported centered probability measures. We describe several operations that allow us to construct additional variance functions from known…
Free exponential families have been previously introduced as a special case of the q-exponential family. We show that free exponential families arise also from a procedure analogous to the definition of exponential families by using the…
Suppose V{\nu} is the pseudo-variance function of the Cauchy-Stieltjes Kernel (CSK) family K+({\nu}) generated by a non degenerate probability measure {\nu} with support bounded from above. We determine the formula for pseudo-variance…
This work proposes algorithms for computing additive and multiplicative free convolutions of two given measures. We consider measures with compact support whose free convolution results in a measure with a density function that exhibits a…
In this paper we specify some facts about the sequence of polynomials associated to a \CSK family and we prove that quadratic variance function is characterized by the property of orthogonality of these polynomials.
We express generalized Cauchy-Stieltjes transforms of some particular Beta distributions (of ultraspherical type generating functions for orthogonal polynomials) as a powered Cauchy-Stieltjes transform of some measure. For suitable values…
We study a family of free stochastic processes whose covariance kernels $K$ may be derived as a transform of a tempered measure $\sigma$. These processes arise, for example, in consideration non-commutative analysis involving free…
In this paper we analyze the covariance kernel of the Gaussian process that arises as the limit of fluctuations of linear spectral statistics for Wigner matrices with a few moments. More precisely, the process we study here corresponds to…
We introduce a finite version of free probability and show the link between recent results using polynomial convolutions and the traditional theory of free probability. One tool for accomplishing this is a seemingly new transformation that…
We prove a Cauchy identity for free quasi-symmetric functions and apply it to the study of various bases. A free Weyl formula and a generalization of the splitting formula are also discussed.
We present a simplified explanation of why free fractional convolution corresponds to the differentiation of polynomials, by finding how the finite free cumulants of a polynomial behave under differentiation. This approach allows us to…
We realize the Belinschi-Nica semigroup of homomorphisms as a free multiplicative subordination. This realization allows to define more general semigroups of homomorphisms with respect to free multiplicative convolution. For these…
In this paper, we show that the kernel function of Cauchy type for type $BC$ intertwines the commuting family of van Diejen's $q$-difference operators. This result gives rise to a transformation formula for certain multiple basic…
We investigate the existence and uniqueness of solutions to first-order Stieltjes differential problems, focusing on the role of the Stieltjes derivative and its kernel. Unlike the classical case, the kernel of the Stieltjes derivative…
Free probability and random matrix theory has shown to be a fruitful combination in many fields of research, such as digital communications, nuclear physics and mathematical finance. The link between free probability and eigenvalue…
We introduce and study a new type of convolution of probability measures called the orthogonal convolution, which is related to the monotone convolution. Using this convolution, we derive alternating decompositions of the free additive…
We characterize by the use of free probability the family of measures for which the mulitiplicative renormalization method applies with $h(x) = (1-x)^_{-1}$. This provides a representation formula for their Voiculescu Transforms.
In this paper we investigate the properties of the free Sheffer systems, which are certain families of martingale polynomials with respect to the free Levy processes. First, we classify such families that consist of orthogonal polynomials;…