Points on nodal lines with given direction

Zeév Rudnick; Igor Wigman

doi:https://doi.org/10.4171/JST/317

Points on nodal lines with given direction

Zeév Rudnick, Igor Wigman

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

We study of the directional distribution function of nodal lines for eigenfunctions of the Laplacian on a planar domain. This quantity counts the number of points where the normal to the nodal line points in a given direction. We give upper bounds for the flat torus, and compute the expected number for arithmetic random waves.

Original language	English
Pages (from-to)	927-953
Number of pages	27
Journal	Journal of Spectral Theory
Volume	10
Issue number	3
DOIs	https://doi.org/10.4171/JST/317
State	Published - 2020

Keywords

Arithmetic random waves
Gradient direction
Nodal line
Toral laplace eigenfunctions
Zero set

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Geometry and Topology

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https://doi.org/10.4171/JST/317

Cite this

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title = "Points on nodal lines with given direction",

abstract = "We study of the directional distribution function of nodal lines for eigenfunctions of the Laplacian on a planar domain. This quantity counts the number of points where the normal to the nodal line points in a given direction. We give upper bounds for the flat torus, and compute the expected number for arithmetic random waves.",

keywords = "Arithmetic random waves, Gradient direction, Nodal line, Toral laplace eigenfunctions, Zero set",

author = "Ze{\'e}v Rudnick and Igor Wigman",

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year = "2020",

doi = "https://doi.org/10.4171/JST/317",

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AU - Rudnick, Zeév

AU - Wigman, Igor

N1 - Publisher Copyright: © European Mathematical Society.

PY - 2020

Y1 - 2020

N2 - We study of the directional distribution function of nodal lines for eigenfunctions of the Laplacian on a planar domain. This quantity counts the number of points where the normal to the nodal line points in a given direction. We give upper bounds for the flat torus, and compute the expected number for arithmetic random waves.

AB - We study of the directional distribution function of nodal lines for eigenfunctions of the Laplacian on a planar domain. This quantity counts the number of points where the normal to the nodal line points in a given direction. We give upper bounds for the flat torus, and compute the expected number for arithmetic random waves.

KW - Arithmetic random waves

KW - Gradient direction

KW - Nodal line

KW - Toral laplace eigenfunctions

KW - Zero set

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DO - https://doi.org/10.4171/JST/317

M3 - مقالة

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VL - 10

SP - 927

EP - 953

JO - Journal of Spectral Theory

JF - Journal of Spectral Theory

IS - 3

ER -

Points on nodal lines with given direction

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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