Volume: 20, Issue: 2(2009)
pp. 227-273 DOI: 10.1142/S0129167X09005261
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Full Text (PDF, 615KB)
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| Title: |
ORBITAL APPROACH TO MICROSTATE FREE ENTROPY |
| Author(s): |
FUMIO HIAI
Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai 980-8579, JapanTAKUHO MIYAMOTO
Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai 980-8579, JapanYOSHIMICHI UEDA
Graduate School of Mathematics, Kyushu University, Fukuoka 810-8560, Japan
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| History: |
Received 13 March 2007
Revised 21 December 2007
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| 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. |
| Keywords: |
Free probability; free entropy; free entropy dimension; mutual free information; non-commutative random variable; free unitary Brownian motion
AMSC numbers:
Primary: 46L54, Secondary: 52C17, Secondary: 28A78, Secondary: 94A17
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