The Tracy-Widom distribution is not infinitely divisible

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• 作者：J. Armando Domí ; nguez-Molina ; ^{jadguez@uas.edu.mx}
• 关键词：Beta Hermite ensembles ; Random matrices ; Largest eigenvalue ; Tail probabilities
• 刊名：Statistics & Probability Letters
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：123
• 期：Complete
• 页码：56-60
• 全文大小：411 K
• 卷排序：123

文摘

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