From discrete to continuous monotone $C^*$-algebras via quantum central   limit theorems
  We prove that all finite joint distributions of creation and annihilation operators in Monotone and anti-Monotone Fock spaces can be realized as Quantum Central Limit of certain operators on a $C^*$-algebra, at least when the test functions are Riemann integrable. Namely, the approximation is given by weighted sequences of creators and annihilators in discrete monotone $C^*$-algebras, the weight being the above cited test functions. The construction is then generalized to processes by an invariance principle. 
Vitonofrio Crismale, Francesco Fidaleo and Yun Gang Lu
math.PR math.OA