Max-convolution semigroups and extreme values in limit theorems for the free multiplicative convolution
Abstract
We investigate relations between additive convolution semigroup and max-convolution semigroup through the law of large numbers for the free multiplicative convolution. Based on the relation, we give a formula related with Belinschi-Nica semigroup and max-Belinschi-Nica semigroup. Finally, we give several limit theorems for classical, free and Boolean extreme values.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2020
- DOI:
- 10.48550/arXiv.2003.05382
- arXiv:
- arXiv:2003.05382
- Bibcode:
- 2020arXiv200305382U
- Keywords:
-
- Mathematics - Probability;
- Mathematics - Functional Analysis;
- Mathematics - Operator Algebras;
- 46L54;
- 46L53;
- 60E07;
- 60G70
- E-Print:
- 26 pages