ORBITAL APPROACH TO MICROSTATE FREE ENTROPY

• HIAI, FUMIO

• MIYAMOTO, TAKUHO

• UEDA, YOSHIMICHI

抄録

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.

収録刊行物

• International Journal of Mathematics

  International Journal of Mathematics 20 (02), 227-273, 2009

  World Scientific

キーワード

• Free probability
• free entropy
• free entropy dimension
• mutual free information
• non-commutative random variable
• free unitary Brownian motion

詳細情報

• CRID: 1050845763745232768
• NII論文ID: 120006714544
• HANDLE: 2237/00030627
• ISSN: 0129167X
• Web Site: https://nagoya.repo.nii.ac.jp/records/28434
• 本文言語コード: en
• 資料種別: journal article
• データソース種別:
  • IRDB
  • CiNii Articles