%0 Journal Article
%T Fluctuations of the nodal length of random spherical harmonics, erratum
%A Igor Wigman
%J Mathematics
%D 2009
%I arXiv
%R 10.1007/s00220-010-1078-8
%X Using the multiplicities of the Laplace eigenspace on the sphere (the space of spherical harmonics) we endow the space with Gaussian probability measure. This induces a notion of random Gaussian spherical harmonics of degree $n$ having Laplace eigenvalue $E=n(n+1)$. We study the length distribution of the nodal lines of random spherical harmonics. It is known that the expected length is of order $n$. It is natural to conjecture that the variance should be of order $n$, due to the natural scaling. Our principal result is that, due to an unexpected cancelation, the variance of the nodal length of random spherical harmonics is of order $\log{n}$. This behaviour is consistent with the one predicted by Berry for nodal lines on chaotic billiards (Random Wave Model). In addition we find that a similar result is applicable for "generic" linear statistics of the nodal lines.
%U http://arxiv.org/abs/0907.1648v3