High Frequency Eigenfunction Immersions and Supremum Norms of Random Waves
Spectral Theory
2015-12-29 v1 Mathematical Physics
Differential Geometry
math.MP
Probability
Abstract
A compact Riemannian manifold may be immersed into Euclidean space by using high frequency Laplace eigenfunctions. We study the geometry of the manifold viewed as a metric space endowed with the distance function from the ambient Euclidean space. As an application we give a new proof of a result of Burq-Lebeau and others on upper bounds for the sup-norms of random linear combinations of high frequency eigenfunctions.
Cite
@article{arxiv.1406.2309,
title = {High Frequency Eigenfunction Immersions and Supremum Norms of Random Waves},
author = {Yaiza Canzani and Boris Hanin},
journal= {arXiv preprint arXiv:1406.2309},
year = {2015}
}
Comments
This article supersedes arXiv:1310.1361, which has now been withdrawn