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- Title
ORBITAL APPROACH TO MICROSTATE FREE ENTROPY.
- Authors
HIAI, FUMIO; MIYAMOTO, TAKUHO; UEDA, YOSHIMICHI
- Abstract
Motivated by Voiculescu's liberation theory, we introduce the orbital free entropy χorb for non-commutative self-adjoint random variables (also for "hyperfinite random multi-variables"). Besides its basic properties, the relation of χorb with the usual free entropy χ is shown. Moreover, the dimension counterpart δ0,orb of χorb is discussed, and we obtain the relation between δ0,orb and the original free entropy dimension δ0 together with applications to δ0 itself.
- Subjects
FREE probability theory; ENTROPY; RANDOM variables; OPERATOR algebras; MATHEMATICAL statistics; MATHEMATICS
- Publication
International Journal of Mathematics, 2009, Vol 20, Issue 2, p227
- ISSN
0129-167X
- Publication type
Article
- DOI
10.1142/S0129167X09005261