From discrete to continuous monotone C^*-algebras via quantum central limit theorems

2016/12/30 by Crismale, Vitonofrio, Fidaleo, Francesco, Lu, Yun Gang
#46L53 #60B99 #60F05 #FOS: Mathematics #Operator Algebras (math.OA) #Probability (math.PR)

paper · doi:10.48550/arxiv.1612.09414

Abstract

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.

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