The Tracy–Widom distribution is not infinitely divisible
Copyright policy )The Tracy–Widom distribution is not infinitely divisible
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 $N \ge 2$ it is proved that the largest eigenvalue of a GOE/GUE random matrix is not infinitely divisible.
Random matrices (probabilistic aspects), tail probabilities, Probability (math.PR), beta Hermite ensembles, FOS: Mathematics, Infinitely divisible distributions; stable distributions, random matrices, largest eigenvalue, Mathematics - Probability
Random matrices (probabilistic aspects), tail probabilities, Probability (math.PR), beta Hermite ensembles, FOS: Mathematics, Infinitely divisible distributions; stable distributions, random matrices, largest eigenvalue, Mathematics - Probability
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).1 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!