q -deformed Poisson random variables on q-Fock space
Naoko Saitoh, Hiroaki Yoshida
The q-deformed Poisson distribution has been introduced as the orthogonalizing probability measure for a certain q-deformation of Charlier polynomials, which is reduced to the usual Poisson distribution in the limit q→1 and takes the free Poisson distribution in case of q=0. We give the operator on the q-Fock space, which has the q-deformed Poisson distribution with respect to the vacuum state. It is a linear combination of a q-number operator, a q-Gaussian random variable, and a scalar operator. This representation is of the same form as of Hudson and Parthasarathy on the symmetric Fock space.
Journal of Mathematical Physics•Aug 1, 2000•17 citations