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arXiv:1203.4530 · Communications in Mathematical Physics

De Finetti Theorem on the CAR Algebra

Vitonofrio Crismale, Francesco Fidaleo

Published May 29, 2012• 26 citations
arXivHTMLPDF
DOI
10.1007/s00220-012-1506-z

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SYMMETRIC STATES ON THE CAR ALGEBRA

Vitonofrio Crismale, Francesco Fidaleo

De Finetti Theorem describes the structure of the symmetric states (i.e. \nexchangeable probability measures) in classical probability. Here we mainly report \ntwo extension of De Finetti Theorem in the case of the CAR algebra. Namely we firstly \nrealize that the compact convex set of such states is a Choquet simplex, whose extremals \nare precisely the product states in the sense of Araki–Moriya. Then we present \na so–called extended version of this result, showing that these states are conditionally \nindependent w.r.t. the tail algebra.

•Jan 1, 2014•0 citations
De Finetti Theorem describes the structure of the symmetric states (i.e. \nexchangeable probability measures) in classical probability. Here we mainly report \ntwo extension of De Finetti Theorem in the case of the CAR algebra. Namely we firstly \nrealize that the compact convex set of such states is a Choquet simplex, whose extremals \nare precisely the product states in the sense of Araki–Moriya. Then we present \na so–called extended version of this result, showing that these states are conditionally \nindependent w.r.t. the tail algebra.