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math-ph2005★ 1 cited
Random discrete Schrödinger operators from Random Matrix Theory
Jonathan Breuer, Peter J. Forrester, Uzy Smilansky
We investigate random, discrete Schrödiner operators which arise naturally in the theory of random matrices, and depend parametrically on Dyson's Coulomb gas inverse temperature $β…
nlin.SI2005★ 11 cited
Nodal domain distribution of rectangular drums
U. Smilansky, R. Sankaranarayanan
We consider the sequence of nodal counts for eigenfunctions of the Laplace-Beltrami operator in two dimensional domains. It was conjectured recently that this sequence stores some…