On toral eigenfunctions and the random wave model

2013/03/12 by Bourgain, Jean
#11P21 #58J50 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1303.2881

Abstract

The purpose of this Note is to provide a deterministic implementation of the random wave model for the number of nodal domains in the context of the two-dimensional torus. The approach is based on recent work due to Nazarov and Sodin and arithmetical properties of lattice points on circles.

Related

• Nodal length fluctuations for arithmetic random waves
• Intermediate and small scale limiting theorems for random fields
• Nodal intersections for random eigenfunctions on the torus
• Variation of the Nazarov-Sodin constant for random plane waves and arithmetic random waves
• Counting nodal domains