243 citations · 573 across the 28 of their papers we have counts for
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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…
Complex determinantal processes and H1 noise
Brian Rider, Balint Virag
For the plane, sphere, and hyperbolic plane we consider the canonical invariant determinantal point processes with intensity rho dnu, where nu is the corresponding invariant measur…
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…
The noise in the circular law and the Gaussian free field
Brian Rider, Balint Virag
Fill an n x n matrix with independent complex Gaussians of variance 1/n. As n approaches infinity, the eigenvalues {z_k} converge to a sum of an H^1-noise on the unit disk and an i…