TL;DR
This paper provides a lower estimate for orbital free entropy under unitary conjugation and demonstrates that the conjectural formula linking it to free entropy does not hold in general, especially beyond hyperfinite cases.
Contribution
It introduces a lower bound for orbital free entropy and shows the failure of the conjectural relationship with free entropy in non-hyperfinite cases.
Findings
Lower estimate of $ ext{chi}_ ext{orb}$ under unitary conjugation
The conjectural formula linking $ ext{chi}_ ext{orb}$ and $ ext{chi}$ generally fails
Breaks in the relationship are observed outside hyperfinite cases
Abstract
A lower estimate of the orbital free entropy under unitary conjugation is proved, and it together with Voiculescu's observation shows that the conjectural exact formula relating to the free entropy breaks in general in contrast to the case when given random multi-variables are all hyperfinite.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.