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Gelfand-Raikov representations of Coxeter groups associated with positive definite norm functions

Bożejko M., Hirai T.

Probability and Mathematical Statistics

2014

Vol. 34, Fasc. 1

161--180

The main purpose of the paper is to study the type of Gelfand-Raikov representations of Coxeter groups (W, S) for the special positive definite functions coming from the deformed Poisson (Haagerup) positive definite functions qL(w) for some special length (norm) functions L on Coxeter groups W.

On free infinite divisibility for classical Meixner distributions

Bożejko M., Hasebe T.

Probability and Mathematical Statistics

2013

Vol. 33, Fasc. 2

363--375

We prove that symmetric Meixner distributions, whose probability densities are proportional to |Γ(t + ix)|2, are freely infinitely divisible for 0 < t ≤ 1/2. The case t = 1/2 corresponds to the law of Lévy’s stochastic area whose probability density is 1/cosh(πx). A logistic distribution, whose probability density is proportional to 1/cosh2(πx), is also freely infinitely divisible.

Deformed fock spaces, Hecke operators and monotone Fock space of Muraki

Bożejko M.

Demonstratio Mathematica

2012

Vol. 45, nr 2

399-414

The main purpose of this paper is to extend our previous construction of T-Fock spaces from a given Yang-Baxter operator satisfying the inequalities (…) to the constructions of T-symmetric Fock spaces related to the class of Yang-Baxter-Hecke operators meeting a weaker condition that (…) .The new representation of the monotone Fock space of N.Muraki will be given. The main idea of this paper is the new class of generalized Gaussian random variables acting on suitable T-symmetric Fock spaces. Relations with the row and column operator space will be also given.