English

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.

Keywords

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This article supersedes arXiv:1310.1361, which has now been withdrawn

R2 v1 2026-06-22T04:34:22.303Z