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- W2549706386 abstract "In this paper, we investigate the small scale equidistribution properties of randomised sums of Laplacian eigenfunctions (i.e. random waves) on a compact manifold. We prove small scale expectation and variance results for random waves on all compact manifolds. Here, small scale refers to balls of radius $r(lambda)to 0$ such that $r/r_{text{Planck}}toinfty$, where $r_{text{Planck}}$ is the Planck scale. For balls at a larger scale (although still $r(lambda)to 0$) we also obtain estimates showing that the probability that a random wave fails to equidistribute decays exponentially with the eigenvalue." @default.
- W2549706386 created "2016-11-30" @default.
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- W2549706386 date "2016-11-18" @default.
- W2549706386 modified "2023-09-24" @default.
- W2549706386 title "Equidistribution of random waves on small balls" @default.
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- W2549706386 doi "https://doi.org/10.48550/arxiv.1611.05983" @default.
- W2549706386 hasPublicationYear "2016" @default.
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