Variation of the Nazarov-Sodin constant for random plane waves and arithmetic random waves

2017/07/03 by Kurlberg, Par, Wigman, Igor
#58C40 #60G60 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1707.00766

Abstract

This is a manuscript containing the full proofs of results announced in [KW], together with some recent updates. 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.

Related

• Nodal length fluctuations for arithmetic random waves
• Intermediate and small scale limiting theorems for random fields
• On toral eigenfunctions and the random wave model
• Concentration for nodal component count of Gaussian Laplace eigenfunctions
• Quantitative limit theorems for local functionals of arithmetic random\n waves