The Tracy-Widom distribution is not infinitely divisible

2016/01/12 by Domínguez-Molina, J. Armando
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1601.02898

Abstract

The classical infinite divisibility of distributions related to eigenvalues of some random matrix ensembles is investigated. It is proved that the β-Tracy-Widom distribution, which is the limiting distribution of the largest eigenvalue of a β-Hermite ensemble, is not infinitely divisible. Furthermore, for each fixed N ≥ 2 it is proved that the largest eigenvalue of a GOE/GUE random matrix is not infinitely divisible.

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