Quantization of the Boolean Poisson Central Limit Theorem and a Generalized Boolean Bernoulli Sequence

This paper is devoted to setting up a quantization of the Boolean Poisson central limit theorem. A sequence of the Boolean independent binomial random variables on an interacting Fock space is constructed in terms of creation–annihilation operators. By using these random variables, we study the Boolean Bernoulli sequence, its generalization and moreover, a quantization of the Poisson central limit theorem with respect to the convergence both in mixed–moments and in law.