Quantization of the Monotone Poisson Central Limit Theorem

In the present paper, we quantize the monotone (as well as anti–monotone) Poisson central limit theorem. One constructs a sequence of monotone independent binomial random ariables in terms of the creation–annihilation operators on a specific interacting Fock space. By using these random variables, one sets up a quantization of the monotone Poisson central limit theorem with respect to the convergence both in mixed–moments and in law, which includes the monotone Laplace–de Moivre CLT as a part. Moreover, one represents the above limit in terms of creation–annihilation operators on the continuous monotone Fock space over L2([0, 1]).