The harmonic ensemble achieves optimal Wasserstein equidistribution rates on homogeneous manifolds of dimension d≥3 and two-point homogeneous manifolds, with similar results for the spherical ensemble and GAF zeros.
H\" o rmander, The spectral function of an elliptic operator
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The survey describes eigenvalue inequalities, spectral asymptotics, nodal domains, and new phenomena for the Dirichlet-to-Neumann map of the Helmholtz equation that do not appear in the Laplace case.
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Equidistribution of points in the Harmonic ensemble for the Wasserstein distance
The harmonic ensemble achieves optimal Wasserstein equidistribution rates on homogeneous manifolds of dimension d≥3 and two-point homogeneous manifolds, with similar results for the spherical ensemble and GAF zeros.
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Spectral properties of the Dirichlet-to-Neumann map for the Helmholtz equation
The survey describes eigenvalue inequalities, spectral asymptotics, nodal domains, and new phenomena for the Dirichlet-to-Neumann map of the Helmholtz equation that do not appear in the Laplace case.