19 citations · 113 across the 18 of their papers we have counts for
18 papers
The Boolean quadratic forms and tangent law
Wiktor Ejsmont, Patrycja Hęćka
In \cite{EjsmontLehner:2020:tangent} we study the limit sums of free commutators and anticommutators and show that the generalized tangent function d…
The Double Fock Space of Type B
Marek Bożejko, Wiktor Ejsmont
In this article, we introduce the notion of a double Fock space of type B. We will show that this new construction is compatible with combinatorics of counting positive and negativ…
A test for normality and independence based on characteristic function
Wiktor Ejsmont, Bojana Milošević, Marko Obradović
In this article we prove a generalization of the Ejsmont characterization of the multivariate normal distribution. Based on it, we propose a new test for independence and normality…
Reflection length with two parameters in the asymptotic representation theory of type B/C and applications
Marek Bożejko, Maciej Dołęga, Wiktor Ejsmont +1
We introduce a two-parameter function on the infinite hyperoctahedral group, which is a bivariate refinement of the reflection length keeping track of the long and th…
Fock space associated with quadrabasic Hermite orthogonal polynomials
Wiktor Ejsmont
This paper introduces a new idea for constructing operators associated with a certain class of probability measures. Special cases include several know classical and noncommutative…
The Free Tangent Law
Wiktor Ejsmont, Franz Lehner
Nevanlinna-Herglotz functions play a fundamental role for the study of infinitely divisible distributions in free probability. In the present paper we study the role of the tangent…
The Trace Method for Cotangent Sums
Wiktor Ejsmont, Franz Lehner
This paper presents a combinatorial study of sums of integer powers of the cotangent which is a popular theme in classical calculus. Our main tool the realization of cotangent valu…
Sums of Commutators in Free Probability
Wiktor Ejsmont, Franz Lehner
We study the linear span of commutators of free random variables and show that these are the only quadratic forms which satisfy the following equivalent properties: * preservation…
Poisson type operators on the Fock space of type B and in the Blitvi{ć} model
Wiktor Ejsmont
In \cite{Bia97} Biane proposed a new statistic on set partitions which he called \emph{restricted crossings}. In a series of papers \cite{Ans01,Ans04,Ans04b,Ans05} Anshelevich show…
Type B Gaussian Statistics as Noncommutative Central Limits
Natasha Blitvić, Wiktor Ejsmont
We show that the noncommutative central limit theorem of Speicher can be adapted to produce the Gaussian statistics associated to Coxeter groups of type B, in the sense of Bożejko,…
Central limit theorem associated to Gaussian operators of type B
Wiktor Ejsmont
In this article we formulate the CLT associated to Gaussian operators of type B -- see \cite{BEH15}, where important role is played by colored pair partitions. Then we present a ce…
Noncommutative probability of type D
Marek Bożejko, Wiktor Ejsmont, Takahiro Hasebe
We construct a deformed Fock space and a Brownian motion coming from Coxeter groups of type D. The construction is analogous to that of the -Fock space (of type A) and the $(α,q…
Sample Variance in Free Probability
Wiktor Ejsmont, Franz Lehner
Let denote i.i.d.~centered standard normal random variables, then the law of the sample variance is the -distribution w…
A Characterization of the Normal Distribution by the Independence of a Pair of Random Vectors
Wiktor Ejsmont
Kagan and Shalaevski 1967 have shown that if the random variables are independent and identically distributed and the distribution of $a_i…
Convolution, subordination and characterization problems in noncommutative probability
Wiktor Ejsmont, Uwe Franz, Kamil Szpojankowski
Characterization problems in free probability are studied here. Using subordination of free additive and free multiplicative convolutions we generalize some known characterizations…
Fock space associated to Coxeter group of type B
Marek Bożejko, Wiktor Ejsmont, Takahiro Hasebe
In this article we construct a generalized Gaussian process coming from Coxeter groups of type B. It is given by creation and annihilation operators on an -Fock space, which…
New characterization of two-state normal distribution
Wiktor Ejsmont
In this article we give a purely noncommutative criterion for the characterization of two-state normal distribution. We prove that families of two-state normal distribution can be…
Characterizations of some free random variables by properties of conditional moments of third degree polynomials
Wiktor Ejsmont
We investigate Laha-Lukacs properties of noncommutative random variables (processes). We prove that some families of free Meixner distributions can be characterized by the conditio…