平面域上随机波的开节线计数
数学物理
2009-03-18 v4 math.MP
概率论
摘要
我们计算了光滑平面域上随机波的开节线数量的渐近期望。我们发现，对于长能量窗口 和短能量窗口 ，当 时，开节线的期望数量与 成正比。我们的结果与 Blum、Gnutzmann 和 Smilansky 在物理学文献中的预测一致 \cite{BGS}。
引用
@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}
}
备注
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