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

Maxime Ingremeau; Alejandro Rivera

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

Mathematical Physics 2018-09-14 v2 math.MP Probability Spectral Theory

Authors: Maxime Ingremeau , Alejandro Rivera

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.

Keywords

nodal domains random monochromatic plane waves bogomolny-schmit constant lower bound expected number

Cite

@article{arxiv.1803.02228,
  title  = {A lower bound for the Bogomolny-Schmit constant for random monochromatic plane waves},
  author = {Maxime Ingremeau and Alejandro Rivera},
  journal= {arXiv preprint arXiv:1803.02228},
  year   = {2018}
}

Comments

6 pages, correction of a computation error and of the proof of lemma 2.2, the main result is stronger than in the original version

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

Abstract

Keywords

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