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Contents of PMS, Vol. 29, Fasc. 2,
pages 251 - 269
 

INDEPENDENCE ARISING FROM INTERACTING FOCK SPACES AND RELATED CENTRAL LIMIT THEOREM

Anis Ben Ghorbal
Vitonofrio Crismale

Abstract: 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.

2000 AMS Mathematics Subject Classification: Primary: 60B99, 46L53; Secondary: 81S05.

Keywords and phrases: Interacting Fock spaces, central limit theorems, GNS representation.

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