We examine, for− 1< q< 1, q-Gaussian processes, ie families of operators (non-commutative
random variables)–where the at fulfill the q-commutation relations for some covariance …

Commutation Relations, Normal Ordering, and Stirling Numbers Page 1 Commutation
Relations, Normal Ordering, and Stirling Numbers Toufik Mansour • Matthias Schork Mansour • …

It is a great pleasure for me that the new Springer Quantum Probability Programmeisopenedbythepresentmonogra…
Obata. In fact this book epitomizes several distinctive features of contemporary quantum …

The book is devoted to the mathematical foundations of nonextensive statistical mechanics.
This is the first book containing the systematic presentation of the mathematical theory and …

A common problem is that of describing the probability distribution of a single, continuous
variable. A few distributions, such as the normal and exponential, were discovered in the …

Given a weighted ℓ2 space with weights associated with an entire function, we consider
pairs of weighted shift operators, whose commutators are diagonal operators, when …

Such functions bear various names: They are said to be holomorphic in Ω, or analytic in Ω;
the terms C-differentiable, differentiable and regular are also used. A key result in the theory …

We present a study of the Gaussian q-measure introduced by Díaz and Teruel from a
probabilistic and from a combinatorial viewpoint. A main motivation for the introduction of the …

We introduce the quadratic harness condition and show that integrable quadratic harnesses
have orthogonal martingale polynomials with a three step recurrence that satisfies a $ q …

The of these cumulants was studied by Lassalle using symmetric functions and
hypergeometric series. We show that the underlying combinatorics is explained through the …