On the number of nodal domains of toral eigenfunctions

Abstract

We study the number of nodal domains of toral Laplace eigenfunctions. Following Nazarov-Sodin's results for random fields and Bourgain's de-randomisation procedure we establish a precise asymptotic result for "generic" eigenfunctions. Our main results in particular imply an optimal lower bound for the number of nodal domains of generic toral eigenfunctions.

34 pages, minor corrections

References in corpus (1)

• Asymptotic laws for the spatial distribution and the number of connected components of zero sets of Gaussian random functions

Cited by in corpus (8)

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• Nodal set of monochromatic waves satisfying the Random Wave Model
• Mass distribution for toral eigenfunctions via Bourgain's de-randomisation