Non-universality of the Nazarov-Sodin constant

Abstract

We prove that the Nazarov-Sodin constant, which up to a natural scaling gives the leading order growth for the expected number of nodal components of a random Gaussian field, genuinely depends on the field. We then infer the same for "arithmetic random waves", i.e. random toral Laplace eigenfunctions.

7 pages. Corrected typos

References in corpus (1)

• On probability measures arising from lattice points on circles

Cited by in corpus (4)

• Nodal portraits of quantum billiards: Domains, lines, and statistics
• On the number of nodal domains of toral eigenfunctions
• Asymptotic laws for the spatial distribution and the number of connected components of zero sets of Gaussian random functions
• The Number of Nodal Components of Arithmetic Random Waves