2024-03-29T04:38:11Z
https://nagoya.repo.nii.ac.jp/oai
oai:nagoya.repo.nii.ac.jp:00028434
2023-01-16T04:21:18Z
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ORBITAL APPROACH TO MICROSTATE FREE ENTROPY
HIAI, FUMIO
MIYAMOTO, TAKUHO
UEDA, YOSHIMICHI
open access
Electronic version of an article published as [International Journal of Mathematics. v.20, n.2, 2009, p.227-273] [http://doi.org/10.1142/S0129167X09005261] © [copyright World Scientific Publishing Company] [https://www.worldscientific.com/worldscinet/ijm]
Free probability
free entropy
free entropy dimension
mutual free information
non-commutative random variable
free unitary Brownian motion
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.
World Scientific
2009
eng
journal article
AM
http://hdl.handle.net/2237/00030627
https://nagoya.repo.nii.ac.jp/records/28434
https://doi.org/10.1142/S0129167X09005261
0129-167X
International Journal of Mathematics
20
02
227
273
https://nagoya.repo.nii.ac.jp/record/28434/files/0702745.pdf
application/pdf
482.2 kB
2019-08-28