Local Universality for Zeros and Critical Points of Monochromatic Random Waves

Yaiza Canzani, Boris Hanin

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

This paper concerns the asymptotic behavior of zeros and critical points for monochromatic random waves ϕλ of frequency λ on a compact, smooth, Riemannian manifold (M, g) as λ→ ∞. We prove global variance estimates for the measures of integration over the zeros and critical points of ϕλ. These global estimates hold for a wide class of manifolds—for example when (M, g) has no conjugate points—and rely on new local variance estimates on zeros and critical points of ϕλ in balls of radius ≈ λ- 1 around a fixed point. Our local results hold under conditions about the structure of geodesics that are generic in the space of all metrics on M.

Original languageEnglish (US)
Pages (from-to)1677-1712
Number of pages36
JournalCommunications In Mathematical Physics
Volume378
Issue number3
DOIs
StatePublished - Sep 1 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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