On the Matsumoto-Yor property in free probability
Kamil Szpojankowski
TL;DR
This paper explores the Matsumoto-Yor property within free probability, demonstrating that certain matrix distributions exhibit this property and characterizing these distributions through regression properties.
Contribution
It establishes the free Matsumoto-Yor property for GIG matrices and Marchenko-Pastur distribution, providing a new characterization in free probability.
Findings
GIG matrices and Marchenko-Pastur distribution have the free Matsumoto-Yor property
Distribution characterized by regression properties in free probability
Limiting empirical eigenvalue distribution analyzed
Abstract
We study the Matsumoto-Yor property in free probability. We prove that the limiting empirical eigenvalue distribution of the GIG matrices and the Marchenko-Pastur distribution have the free Matsumoto-Yor property. Finally we characterize these distributions by a regression properties in free probability.
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.