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math.PR2006
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…
math.PR2006★ 243 cited
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…