The Tracy-Widom distribution is not infinitely divisible
Probability
2016-01-13 v1
Abstract
The classical infinite divisibility of distributions related to eigenvalues of some random matrix ensembles is investigated. It is proved that the -Tracy-Widom distribution, which is the limiting distribution of the largest eigenvalue of a -Hermite ensemble, is not infinitely divisible. Furthermore, for each fixed it is proved that the largest eigenvalue of a GOE/GUE random matrix is not infinitely divisible.
Cite
@article{arxiv.1601.02898,
title = {The Tracy-Widom distribution is not infinitely divisible},
author = {J. Armando Domínguez-Molina},
journal= {arXiv preprint arXiv:1601.02898},
year = {2016}
}