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.
Shrinking scale equidistribution for monochromatic random waves on compact manifolds
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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.