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

2018/03/06 by Ingremeau, Maxime, Rivera, Alejandro
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1803.02228

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 πR² 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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