Counting open nodal lines of random waves on planar domains
Mathematical Physics
2009-03-18 v4 math.MP
Probability
Abstract
We compute the asymptotic expectation of the number of {\em open} nodal lines for random waves on smooth planar domains. We find that for both the long energy window and the short one the expected number of open nodal lines is proportional to , asymptotically as . Our results are consistent with the predictions in the physics literature made by Blum, Gnutzmann and Smilansky \cite{BGS}.
Cite
@article{arxiv.0810.1276,
title = {Counting open nodal lines of random waves on planar domains},
author = {John A. Toth and Igor Wigman},
journal= {arXiv preprint arXiv:0810.1276},
year = {2009}
}
Comments
1) We simplified the proof of the converse direction in Lemma 2.1. 2) We moved the proof of Prop. 3.2 (and Lemma 3.1) to the appendix and just stated the main results in section 3.2. We also added two references [BSZ1],[BSZ2] to papers by Bleher, Shiffman and Zeldtich in section 3.2. 3) Added references to papers about nodal volume and Yau's conjecture