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arXiv · 1910.04001

Random moments for the new eigenfunctions of point scatterers on rectangular flat tori

Thomas Letendre·Henrik Ueberschär
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Abstract

We define a random model for the moments of the new eigenfunctions of a point scat-terer on a 2-dimensional rectangular flat torus. In the deterministic setting,Seba conjectured these moments to be asymptotically Gaussian, in the semi-classical limit. This conjecture was disproved by Kurlberg-Uebersch{\"a}r on Diophantine tori. In our model, we describe the accumulation points in distribution of the randomized moments, in the semi-classical limit. We prove that asymptotic Gaussianity holds if and only if some function, modeling the multiplicities of the Laplace eigenfunctions, diverges to +$\infty$.

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Thomas Letendre, Henrik Ueberschär. 2019-10-09. Random moments for the new eigenfunctions of point scatterers on rectangular flat tori. https://doi.org/10.1007/s00023-021-01032-5

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