随机球谐函数节点长度的涨落，勘误
概率论
2015-05-13 v3 数学物理
math.MP
摘要
利用球面上拉普拉斯本征空间（球谐函数空间）的重数，我们赋予该空间高斯概率测度。这引出了度数为、拉普拉斯本征值为的随机高斯球谐函数的概念。我们研究了随机球谐函数节点线的长度分布。已知期望长度为量级。由于自然标度，自然可以猜想方差应为量级。我们的主要结果是，由于一种意外的抵消，随机球谐函数节点长度的方差为量级。这一行为与Berry对混沌台球（随机波模型）节点线所预测的行为一致。此外，我们发现类似的结果也适用于节点线的“一般”线性统计量。
引用
@article{arxiv.0907.1648,
title = {Fluctuations of the nodal length of random spherical harmonics, erratum},
author = {Igor Wigman},
journal= {arXiv preprint arXiv:0907.1648},
year = {2015}
}
备注
This is to correct a sign mistake that has been made in the previous version (that was published in Comm. Math. Phys.). As a result the leading constant in all the theorems was wrong, and the constants are now consistent with the one predicted by Berry. A corrected manuscript plus a detailed erratum with all the corrections that were made relatively to the version published is attached