A lower bound for the Bogomolny-Schmit constant for random monochromatic plane waves. (arXiv:1803.02228v2 [math-ph] UPDATED)

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. 查看全文>>