243 citations · 330 across the 10 of their papers we have counts for
6 papers · 1 filter
Spiking the random matrix hard edge
Jose A. Ramirez, Brian Rider
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…
Hard edge tail asymptotics
Jose A. Ramirez, Brian Rider, Ofer Zeitouni
Let be the limiting smallest eigenvalue in the general (β, a)-Laguerre ensemble of random matrix theory. Here β>0, a >-1; for β=1,2,4 and integer a, this object governs the sin…
Bulk universality for Wigner hermitian matrices with subexponential decay
Laszlo Erdos, Jose Ramirez, Benjamin Schlein +3
We consider the ensemble of Wigner hermitian matrices that generalize the Gaussian unitary ensemble (GUE). The matrix element…
Diffusion at the random matrix hard edge
Jose A. Ramirez, Brian Rider
We show that the limiting minimal eigenvalue distributions for a natural generalization of Gaussian sample-covariance structures (the "beta ensembles") are described by the spectru…
Shape of the ground state energy density of Hill's equation with nice Gaussian potential
Jose A. Ramirez, Brian Rider
Consider Hill's operator Q = -D^2 + q(x) in which the potential q(x) is an almost surely continuous and rotation invariant Gaussian process on the circle of perimeter one. Viewing…
Beta ensembles, stochastic Airy spectrum, and a diffusion
Jose Ramirez, Brian Rider, Balint Virag
We prove that the largest eigenvalues of the beta ensembles of random matrix theory converge in distribution to the low-lying eigenvalues of the random Schroedinger operator -d^2/d…