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Random eigenfunctions on flat tori: universality for the number of intersections. (English) Zbl 1462.53031

Summary: We show that several statistics of the number of intersections between random eigenfunctions of general eigenvalues and a given smooth curve in flat tori are universal under various families of randomness.

MSC:

53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
35P15 Estimates of eigenvalues in context of PDEs
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