Orbital approach to microstate free entropy

Fumio Hiai, Takuho Miyamoto, Yoshimichi Ueda

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)227-273
Number of pages47
JournalInternational Journal of Mathematics
Issue number2
Publication statusPublished - Feb 2009

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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