Small-scale equidistribution for random spherical harmonics
classification
🧮 math.PR
keywords
sphericalharmonicsrandomsmallareaassignedcomparediscrepancy
read the original abstract
We study random spherical harmonics at shrinking scales. We compare the mass assigned to a small spherical cap with its area, and find the smallest possible scale at which, with high probability, the discrepancy between them is small simultaneously at every point on the sphere.
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Cited by 2 Pith papers
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Sign-balance of random Laplace eigenfunctions
Random eigenfunctions of the Laplace operator are sign-balanced above a precisely determined scale (optimal up to log factors of the energy) with almost full probability.
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Sign-balance of random Laplace eigenfunctions
Random eigenfunctions are sign-balanced above a precisely determined scale (optimal up to log factors in energy) with almost full probability, including for spherical harmonics and band-limited waves on smooth manifolds.
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