Igor Wigman: The defect variance of random spherical harmonics
Igor Wigman, University of Cardiff
Tid: Ti 2012-01-17 kl 14.30
Plats: Room 3721
This work is joint with Domenico Marinucci (Rome Tor Vergata).
The defect of a function $f:M\rightarrow \mathbb{R}$ is defined as the
difference between the measure of the positive and negative regions. In
this paper, we begin the analysis of the distribution of defect of
random Gaussian spherical harmonics. By an easy argument, the defect is
non-trivial only for even degree and the expected value always
vanishes. Our principal result is obtaining the asymptotic shape of the
defect variance, in the high frequency limit. As other geometric
functionals of random eigenfunctions, the defect may be used as a tool
to probe the statistical properties of spherical random fields, a topic
of great interest for modern Cosmological data analysis.