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arXiv · 1803.02228

A lower bound for the Bogomolny-Schmit constant for random monochromatic plane waves

Maxime Ingremeau·Alejandro Rivera
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Abstract

This note deals with nodal domains of random monochromatic plane waves. It was shown by Nazarov and Sodin that the expected number of such nodal domains included in a disk of radius $R$ is proportional to $\pi R^2$ in the large $R$ limit. However, very little is known on the value of the proportionality constant from a mathematical point of view. The aim of this note is to obtain a lower bound on the value of this constant my elementary means.

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Maxime Ingremeau, Alejandro Rivera. 2018-03-06. A lower bound for the Bogomolny-Schmit constant for random monochromatic plane waves. https://arxiv.org/abs/1803.02228

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