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A constructive Boolean central limit theorem. (English) Zbl 1139.60009

In this paper proper constructive quantum stochastic processes (namely creation-annihilation-number processes) on the Boolean Fock space and with discrete time are defined.
The main result is: a quantum central limit argument is used to get the creation-annihilation-number processes on the Boolean Fock space starting from discrete-time processes. The constructive approach shows that discrete-time processes give exactly a particular pair partition, i.e. interval partition.
The main difference between results of the paper and preceding papers on the subject is a concrete construction instead of existence theorems.

MSC:

60B99 Probability theory on algebraic and topological structures
46L53 Noncommutative probability and statistics
60F05 Central limit and other weak theorems
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