Article ID Journal Published Year Pages File Type
8900039 Journal of Mathematical Analysis and Applications 2018 25 Pages PDF
Abstract
The Berry heuristic has been a long standing ansatz about the high energy (i.e. large eigenvalues) behaviour of eigenfunctions (see [7]). Roughly speaking, it states that under some generic boundary conditions, these eigenfunctions exhibit Gaussian behaviour when the eigenvalues grow to infinity. Our aim in this paper is to make this statement quantitative and to establish some rigorous bounds on the distance to Gaussianity, focussing on the hyperspherical case (i.e., for eigenfunctions of the Laplace-Beltrami operator on the normalized d-dimensional sphere - also known as spherical harmonics). Some applications to non-Gaussian models are also discussed.
Related Topics
Physical Sciences and Engineering Mathematics Analysis
Authors
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