17 citations · 62 across the 14 of their papers we have counts for
19 papers
Quadratic embedding constants of path graphs
Wojciech Młotkowski
We characterize positive definiteness for some family of matrices. As an application we derive explicit value of the quadratic embedding constants of the path graphs.
Probability distributions with rational free -transform
Wojciech Młotkowski
We study the class of those probability distributions for which the free -transforms are rational functions. This class is closed under the additi…
On freely quasi-infinitely divisible distributions
Ikkei Hotta, Wojciech Młotkowski, Noriyoshi Sakuma +1
Inspired by the notion of quasi-infinite divisibility (QID), we introduce and study the class of freely quasi-infinitely divisible (FQID) distributions on , i.e. distri…
Free self-decomposability and unimodality of the Fuss-Catalan distributions
Wojciech Młotkowski, Noriyoshi Sakuma, Yuki Ueda
We study properties of the Fuss-Catalan distributions , , : free infinite divisibility, free self-decomposability, free regularity and unimodality. We sh…
Some relatives of the Catalan sequence
Elżbieta Liszewska, Wojciech Młotkowski
We study a family of sequences , where and are real parameters. We find a sufficient condition for positive definiteness of the sequen…
Permutations of type with fixed number of descents and minus signs
Katarzyna Kril, Wojciech Młotkowski
We study three dimensional array of numbers , , where is the number of type permutations of order with descents and minus signs.…
On Quadratic Embedding Constants of Star Product Graphs
Wojciech Młotkowski, Nobuaki Obata
A connected graph is of QE class if it admits a quadratic embedding in a Hilbert space, or equivalently if the distance matrix is conditionally negative definite, or equivalent…
Cauchy-Stieltjes families with polynomial variance functions and generalized orthogonality
Wlodzimierz Bryc, Raouf Fakhfakh, Wojciech Mlotkowski
This paper studies variance functions of Cauchy-Stieltjes Kernel families generated by compactly supported centered probability measures. We describe several operations that allow…
Positive definite functions on Coxeter groups with applications to operator spaces and noncommutative probability
Marek Bożejko, Światosław R. Gal, Wojciech Młotkowski
A new class of positive definite functions related to colour-length function on arbitrary Coxeter group is introduced. Extensions of positive definite functions, called the Riesz-C…
New Eulerian numbers of type D
Anna Borowiec, Wojciech Młotkowski
We introduce a new array of type Eulerian numbers, different from that studied by Brenti, Chow and Hyatt. We find in particular the recurrence relation, Worpitzky formula and t…
A family of sequences of binomial type
Wojciech Młotkowski, Anna Romanowicz
For delta operator we find the corresponding polynomial sequence of binomial type and relations with Fuss numbers. In the case we show that the cor…
A Fuss-type family of positive definite sequences
Wojciech Młotkowski, Karol A. Penson
We study a two-parameter family of deformations of the Fuss numbers. We show a sufficient condition for positive definiteness of and prove that some of the…
Spectral density of generalized Wishart matrices and free multiplicative convolution
Wojciech Mlotkowski, Maciej A. Nowak, Karol A. Penson +1
We investigate the level density for several ensembles of positive random matrices of a Wishart--like structure, , where stands for a nonhermitian random matrix…
Probability distributions with binomial moments
Wojciech Mlotkowski, Karol A. Penson
We prove that if and then the binomial sequence , , is positive definite and is the moment sequence of a probability measur…
The probability measure corresponding to 2-plane trees
Wojciech Mlotkowski, Karol A. Penson
We study the probability measure for which the moment sequence is . We prove that is absolutely continuous, find the density function an…
Densities of the Raney distributions
Wojciech Mlotkowski, Karol A. Penson, Karol Zyczkowski
We prove that if and then the sequence , , is positive definite, more precisely, is the moment sequence of a probab…
The free Meixner class for pairs of measures
Michael Anshelevich, Wojciech Młotkowski
We investigate in more detail the two-state free convolution semigroups of pairs of measures whose Jacobi parameters are linear in the convolution parameter . These semigroups w…
Semigroups of distributions with linear Jacobi parameters
Michael Anshelevich, Wojciech Młotkowski
We show that a convolution semigroup of measures has Jacobi parameters polynomial in the convolution parameter if and only if the measures come from the Meixner class. Moreover…
Orthogonal polynomials induced by discrete-time quantum walks in one dimension
Masatoshi Hamada, Norio Konno, Wojciech Mlotkowski
In this paper we obtain some properties of orthogonal polynomials given by a weight function which is a limit density of a rescaled discrete-time quantum walk on the line.