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pro vyhledávání: '"Bożejko, Marek"'
Autor:
Bozejko, Marek, Bozejko, Wojciech
This paper is the survey of some of our results related to $q$-deformations of the Fock spaces and related to $q$-convolutions for probability measures on the real line $\mathbb{R}$. The main idea is done by the combinatorics of moments of the measur
Externí odkaz:
http://arxiv.org/abs/2311.06405
Autor:
Bożejko, Marek, Ejsmont, Wiktor
Publikováno v:
SIGMA 19 (2023), 040, 22 pages
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 negative inversions on a hyperoctahedral group.
Comment: Section 2 parti
Comment: Section 2 parti
Externí odkaz:
http://arxiv.org/abs/2202.13762
We introduce a two-parameter function $\phi_{q_+,q_-}$ on the infinite hyperoctahedral group, which is a bivariate refinement of the reflection length keeping track of the long and the short reflections separately. We show that this signed reflection
Externí odkaz:
http://arxiv.org/abs/2104.14530
Publikováno v:
In Journal of Functional Analysis 1 March 2023 284(5)
Akademický článek
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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-Coxeter product, from the Riesz product on the Rademacher (Abelian Coxe
Externí odkaz:
http://arxiv.org/abs/1704.06845
Publikováno v:
Internat. J. Math. 28 (2017), no. 2, 1750010, 30 pp
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 $q$-Fock space (of type A) and the $(\alpha,q)$-Fock space (of type B).
Comment: 25 pages, 8 figures, maj
Comment: 25 pages, 8 figures, maj
Externí odkaz:
http://arxiv.org/abs/1609.01049
We consider Fock representations of the $Q$-deformed commutation relations $$\partial_s\partial^\dag_t=Q(s,t)\partial_t^\dag\partial_s+\delta(s,t), \quad s,t\in T.$$ Here $T:=\mathbb R^d$ (or more generally $T$ is a locally compact Polish space), the
Externí odkaz:
http://arxiv.org/abs/1603.03075
Let $\sigma$ be a non-atomic, infinite Radon measure on $\mathbb R^d$, for example, $d\sigma(x)=z\,dx$ where $z>0$. We consider a system of freely independent particles $x_1,\dots,x_N$ in a bounded set $\Lambda\subset\mathbb R^d$, where each particle
Externí odkaz:
http://arxiv.org/abs/1603.00208
Publikováno v:
Journal of Mathematical Physics, Vol.57, Issue 2, 021702, 2016
Let $\nu_{\alpha,q}$ be the probability and orthogonality measure for the $q$-Meixner-Pollaczek orthogonal polynomials, which has appeared in \cite{BEH15} as the distribution of the $(\alpha,q)$-Gaussian process (the Gaussian process of type B) over
Externí odkaz:
http://arxiv.org/abs/1512.08862