Cauchy–Stieltjes families with polynomial variance functions and generalized orthogonality

DOI10.19195/0208-4147.39.2.1zbMath1447.60045arXiv1708.05343OpenAlexW2749090813MaRDI QIDQ5109843

Wojciech Młotkowski, Wlodzimierz Bryc, Raouf Fakhfakh

Publication date: 13 May 2020

Published in: Probability and Mathematical Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.05343

zbMATH Keywords

generalized orthogonalityvariance functionsFuss-Catalan numbers\(R\)-transform\(S\)-transformfree multiplicative convolutionfree additive convolutionkernel families

Mathematics Subject Classification ID

Characteristic functions; other transforms (60E10) Exact enumeration problems, generating functions (05A15) Free probability and free operator algebras (46L54) Characterization and structure theory of statistical distributions (62E10)

Related Items (7)

A survey on the effects of free and Boolean convolutions on Cauchy-Stieltjes kernel families ⋮ On polynomials associated with Cauchy–Stieltjes kernel families ⋮ Explicit free multiplicative law of large numbers ⋮ BOOLEAN MULTIPLICATIVE CONVOLUTION AND CAUCHY-STIELTJES KERNEL FAMILIES ⋮ Variance function of Boolean additive convolution ⋮ On some properties of Cauchy-Stieltjes kernel families ⋮ A characterization of the Marchenko-Pastur probability measure

Uses Software

• OEIS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On Cauchy-Stieltjes kernel families
• One-sided Cauchy-Stieltjes kernel families
• On \(d\)-orthogonality of the Sheffer systems associated to a convolution semigroup
• Fuss-Catalan numbers in noncommutative probability
• Natural real exponential families with cubic variance functions
• Laplace transform inversion and Padé-type approximants
• Natural exponential families with quadratic variance functions
• Addition of freely independent random variables
• On a family of approximation operators
• Free martingale polynomials.
• Characterization of quadratic Cauchy-Stieltjes kernel families based on the orthogonality of polynomials
• Shohat-Favard and Chebyshev's methods in \(d\)-orthogonality
• Restricted permutations and queue jumping
• Characterization of the cubic exponential families by orthogonality of polynomials.
• Superconvergence to the central limit and failure of the Cramér theorem for free random variables
• Densities of the Raney distributions
• Characterizations of some polynomial variance functions by \(d\)-pseudo-orthogonality
• Classical scale mixtures of Boolean stable laws
• Free powers of the free Poisson measure
• Free Bessel Laws
• Free Random Variables
• FREE EXPONENTIAL FAMILIES AS KERNEL FAMILIES
• Lectures on the Combinatorics of Free Probability
• L'orthogonalité et les récurrences de polynômes d'ordre supérieur à deux
• GENERATING FUNCTIONS OF CAUCHY–STIELTJES TYPE FOR ORTHOGONAL POLYNOMIALS
• Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations
• On the multiplication of free N -tuples of noncommutative random variables
• A free analogue of Hincin’s characterization of infinite divisibility
• Probability distributions with binomial moments

This page was built for publication: Cauchy–Stieltjes families with polynomial variance functions and generalized orthogonality