On the Excursion Sets of Spherical Gaussian Eigenfunctions

Details On the Excursion Sets of Spherical Gaussian Eigenfunctions On the Excursion Sets of Spherical Gaussian Eigenfunctions

2010-09-22

arxiv.org/abs/1009.4367v1

Mathematics

Probability

Scientific paper

The high frequency behaviour for random eigenfunctions of the spherical Laplacian has been recently the object of considerable interest, also because of strong motivations arising from Physics and Cosmology. In this paper, we are concerned with the high frequency behaviour of excursion sets; in particular, we establish a Uniform Central Limit Theorem for the empirical measure, i.e. the proportion of spherical surface where spherical Gaussian eigenfunctions lie below a level $z$. Our proofs borrows some techniques from the literature on stationary long memory processes; in particular, we expand the empirical measure into Hermite polynomials, and establish a uniform weak reduction principle, entailing that the asymptotic behaviour is asymptotically dominated by a single term in the expansion. As a result, we establish a functional central limit theorem; the limiting process is fully degenerate.

Affiliated with

Also associated with

No associations

Rating

On the Excursion Sets of Spherical Gaussian Eigenfunctions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Excursion Sets of Spherical Gaussian Eigenfunctions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Excursion Sets of Spherical Gaussian Eigenfunctions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-637960