Topology and Nesting of the Zero Set Components of Monochromatic Random Waves

Yaiza Canzani, Peter Sarnak

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

This paper is dedicated to the study of the topologies and nesting configurations of the components of the zero set of monochromatic random waves. We prove that the probability of observing any diffeomorphism type and any nesting arrangement among the zero set components is strictly positive for waves of large enough frequencies. Our results are a consequence of building Laplace eigenfunctions in euclidean space whose zero sets have a component with prescribed topological type or an arrangement of components with prescribed nesting configuration.

Original languageEnglish (US)
Pages (from-to)343-374
Number of pages32
JournalCommunications on Pure and Applied Mathematics
Volume72
Issue number2
DOIs
StatePublished - Feb 1 2019

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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