Free Infinite Divisibility for Ultrasphericals
Octavio Arizmendi, Serban T. Belinschi
TL;DR
This paper proves that integral powers of the semicircular distribution are freely infinitely divisible and provides a new proof of the free infinite divisibility of the Gaussian distribution.
Contribution
It establishes free infinite divisibility for powers of the semicircular distribution and offers an alternative proof for the Gaussian case.
Findings
Integral powers of the semicircular distribution are freely infinitely divisible.
The Gaussian distribution is also shown to be freely infinitely divisible.
Provides new proof techniques for free infinite divisibility.
Abstract
We prove that the integral powers of the semicircular distribution are freely infinitely divisible. As a byproduct we get another proof of the free infnite divisibility of the classical Gaussian distribution.
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.