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.