Fractional free convolution powers
Probability
2021-02-10 v3 Complex Variables
Operator Algebras
Abstract
The extension of the concept of a free convolution power to the case of non-integer was introduced by Bercovici-Voiculescu and Nica-Speicher, and related to the minor process in random matrix theory. In this paper we give two proofs of the monotonicity of the free entropy and free Fisher information of the (normalized) free convolution power in this continuous setting, and also establish an intriguing variational description of this process.
Keywords
Cite
@article{arxiv.2009.01882,
title = {Fractional free convolution powers},
author = {Dimitri Shlyakhtenko and Terence Tao. With an appendix by David Jekel},
journal= {arXiv preprint arXiv:2009.01882},
year = {2021}
}
Comments
37 pages. This is the final version, incorporating referee suggestions. To appear, Indiana U. Math. J