FoCM 2014 conference
Workshop B6 - Random Matrices
December 15, 15:00 ~ 15:25 - Room B12
Deformed smallest singular value laws
Brian Rider
Temple University, US - brian.rider@temple.edu
We characterize the limiting smallest eigenvalue distributions for sample covariance type matrices drawn from a spiked population in terms of random integral operators. From here we derive partial differential equations satisfied by the corresponding distribution functions. We also show that, under a natural limit, these spiked "hard edge" laws degenerate to the critically spiked Tracy-Widom laws of basic importance in mathematical statistics. As a final application we derive a dynamic characterization of the Wishart distribution (which can be viewed as a Dufresne identity for matrix processes).
Joint work with Jose Ramirez (Universidad de Costa Rica) and Benedek Valko (University of Wisconsin - Madison).