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A relation between two different formulations of the Berry's conjecture
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The Random Wave Conjecture of M. V. Berry is the heuristic that eigenfunctions of a classically chaotic system should behave like Gaussian random fields, in the large eigenvalue limit. In this work we collect some definitions and properties of Gaussian random fields, and show that the formulation of the Berry's conjecture proposed using local weak limits is equivalent to the one that is based on the Benjamini-Schramm convergence. Finally, we see that both these formulations of the Berry's property imply another property known as inverse localization that relates high energy eigenfunctions and solutions to the Euclidean Helmholtz equation.
Forward citations
Cited by 2 Pith papers
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Local Weyl law and length-minimising loops on hyperbolic surfaces
For large random hyperbolic surfaces, the pointwise variance of a smoothed local Weyl law equals the Berry random-wave value, up to explicit O(1/(L²g)+1/g²) errors.
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Local limits of high energy eigenfunctions on integrable billiards
Rational rectangles and the three integrable triangles have strong inverse localization, while generic irrational rectangles and (claimed) generic ellipses fail it strongly.
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