The Tracy–Widom distribution is not infinitely divisible

J. Armando Domínguez-Molina

Statistics & Probability Letters, 2017, vol. 123, issue C, 56-60

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.

Keywords: Beta Hermite ensembles; Random matrices; Largest eigenvalue; Tail probabilities (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.spl.2016.11.029

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