An example of a generalized Brownian motion
- M. Bożejko, R. Speicher
- Mathematics
- 1 April 1991
We present an example of a generalized Brownian motion. It is given by creation and annihilation operators on a “twisted” Fock space ofL2(ℝ). These operators fulfill (for a fixed −1≦μ≦1) the…
Convolution and limit theorems for conditionally free random variables
- M. Bożejko, M. Leinert, R. Speicher
- Mathematics
- 17 October 1994
We introduce the notion of a conditionally free product and conditionally free convolution. We describe this convolution both from a combinatorial point of view, by showing its connection with the…
q-Gaussian Processes: Non-commutative and Classical Aspects
- M. Bożejko, B. Kümmerer, R. Speicher
- Mathematics
- 30 April 1996
Abstract: We examine, for −1<q<1, q-Gaussian processes, i.e. families of operators (non-commutative random variables) – where the at fulfill the q-commutation relations for some covariance…
Completely positive maps on Coxeter groups, deformed commutation relations, and operator spaces
- M. Bożejko, R. Speicher
- Mathematics
- 30 August 1994
In this article we prove that quasi-multiplicative (with respect to the usual length function) mappings on the permutation group $\SSn$ (or, more generally, on arbitrary amenable Coxeter groups),…
On a class of free Lévy laws related to a regression problem
- M. Bożejko, W. Bryc
- Mathematics
- 28 October 2004
Interacting Fock Spaces and Gaussianization of Probability Measures
- L. Accardi, M. Bożejko
- Mathematics
- 1 October 1998
We prove that any probability measure on ℝ, with moments of all orders, is the vacuum distribution, in an appropriate interacting Fock space, of the field operator plus (in the nonsymmetric case) a…
Interpolations between bosonic and fermionic relations given by generalized brownian motions
- M. Bożejko, R. Speicher
- Mathematics
- 1 May 1996
We present an interpolation between the bosonic and fermionic relations. This interpolation is given by an object which we call 'generalized Brownian motion' and which is characterized by a…
Positive-definite kernels, length functions on groups and a noncommutative von Neumann inequality
- M. Bożejko
- Mathematics
- 1989
Ψ-INDEPENDENT AND SYMMETRIZED WHITE NOISES
- M. Bożejko, R. Speicher
- Mathematics
- 1 October 1991
Completely positive maps on Coxeter groups and the ultracontractivity of the q-Ornstein-Uhlenbeck semigroup
- M. Bożejko
- Mathematics
- 1998
1. Coxeter groups. In this note we give an application of the following result on the symmetric group Sn: Theorem 1. For fixed n ∈ N let us consider the permutation group Sn and denote by πi ∈ Sn (i…
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