English

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 β\beta-Tracy-Widom distribution, which is the limiting distribution of the largest eigenvalue of a β\beta-Hermite ensemble, is not infinitely divisible. Furthermore, for each fixed N2N \ge 2 it is proved that the largest eigenvalue of a GOE/GUE random matrix is not infinitely divisible.

Keywords

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}
}
R2 v1 2026-06-22T12:27:52.584Z