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Independence arising from interacting Fock spaces and related central limit theorem

Ben Ghorbal A., Crismale V.

Probability and Mathematical Statistics

2009

Vol. 29, Fasc. 2

251--269

We present the notion of projective independence, which abstracts, in an algebraic setting, the factorization rule for the vacuum expectation of creation-annihilations-preservation operators in interacting Fock spaces described in [3]. Furthermore, we give a central limit theorem based on such a notion and a Fock representation of the limit process.