On the Number of Nodal Domains of Toral Eigenfunctions

Jeremiah Buckley; Igor Wigman

doi:10.1007/s00023-016-0476-7

On the Number of Nodal Domains of Toral Eigenfunctions

Jeremiah Buckley^*, Igor Wigman

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-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 language	English
Article number	17
Pages (from-to)	3027–3062
Journal	Annales Henri Poincare
Volume	2016
Early online date	28 Mar 2016
DOIs	https://doi.org/10.1007/s00023-016-0476-7
Publication status	Published - Nov 2016

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title = "On the Number of Nodal Domains of Toral Eigenfunctions",

abstract = "We study the number of nodal domains of toral Laplace eigenfunctions. Following Nazarov–Sodin{\textquoteright}s results for random fields and Bourgain{\textquoteright}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.",

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AU - Wigman, Igor

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AB - 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.

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M3 - Article

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SP - 3027

EP - 3062

JO - Annales Henri Poincare

JF - Annales Henri Poincare

M1 - 17

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On the Number of Nodal Domains of Toral Eigenfunctions

Abstract

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