On the Number of Nodal Domains of Toral Eigenfunctions

Jeremiah Buckley*, Igor Wigman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)

Abstract

We study the number of nodal domains of toral Laplace eigenfunctions. Following Nazarov–Sodin’s results for random fields and Bourgain’s de-randomisation procedure we establish a precise asymptotic result for “generic” eigenfunctions. Our main results in particular imply an optimal lower bound for the number of nodal domains of generic toral eigenfunctions.

Original languageEnglish
Article number17
Pages (from-to)3027–3062
JournalAnnales Henri Poincare
Volume2016
Early online date28 Mar 2016
DOIs
Publication statusPublished - Nov 2016

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