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• W1848812355 abstract "We characterize the limiting smallest eigenvalue distributions (or hard edge laws) for sample covariance type matrices drawn from a spiked population. In the case of a single spike, the results are valid in the context of the general $$beta $$ ensembles. For multiple spikes, the necessary construction restricts matters to real, complex or quaternion ( $$beta =1,2,$$ or 4) ensembles. The limit laws are described in terms of random integral operators, and partial differential equations satisfied by the corresponding distribution functions are derived as corollaries. We also show that, under a natural limit, all spiked hard edge laws derived here degenerate to the critically spiked soft edge laws (or deformed Tracy–Widom laws). The latter were first described at $$beta =2$$ by Baik, Ben Arous, and Peche (Ann Probab 33:1643–1697, 2005), and from a unified $$beta $$ random operator point of view by Bloemendal and Virag (Probab Theory Relat Fields 156:795–825, 2013; Ann Probab arXiv:1109.3704 , 2011)." @default.
• W1848812355 created "2016-06-24" @default.
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• W1848812355 date "2016-08-17" @default.
• W1848812355 modified "2023-10-03" @default.
• W1848812355 title "Spiking the random matrix hard edge" @default.
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• W1848812355 doi "https://doi.org/10.1007/s00440-016-0733-1" @default.
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