Spiking the random matrix hard edge

• Published in: Probability theory and related fields Vol. 169; no. 1-2; pp. 425 - 467
• Main Authors: Ramírez, José A., Rider, Brian
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2017; Springer Nature B.V
• Subjects: Covariance; Deformation; Differential equations; Distribution functions; Economics; Finance; Insurance; Management; Mathematical and Computational Biology; Mathematical and Computational Physics; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Operators (mathematics); Partial differential equations; Probability; Probability Theory and Stochastic Processes; Quantitative Finance; Quaternions; Statistics for Business; Theoretical; 60B20; 60F05

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 β ensembles. For multiple spikes, the necessary construction restr...