Journal article

Nodal intersections for arithmetic random waves against a surface

Abstract:: Given the ensemble of random Gaussian Laplace eigenfunctions on the three-dimensional torus (‘3d arithmetic random waves’), we investigate the one-dimensional Hausdorff measure of the nodal intersection curve against a compact regular toral surface (the ‘nodal intersection length’). The expected length is proportional to the square root of the eigenvalue, times the surface area, independent of the geometry. Our main finding is the leading asymptotic of the nodal intersection length variance, against a surface of non-vanishing Gauss–Kronecker curvature. The problem is closely related to the theory of lattice points on spheres: by the equidistribution of the lattice points, the variance asymptotic depends only on the geometry of the surface.

Publication status:: Published

Peer review status:: Peer reviewed

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APA Style

Maffucci, R. (2019). Nodal intersections for arithmetic random waves against a surface. Annales Henri Poincare, 20(1), 3651–3691.

MLA Style

Maffucci, R. “Nodal Intersections for Arithmetic Random Waves against a Surface.” Annales Henri Poincare, vol. 20, no. 1, Springer, 2019, pp. 3651–91.

Chicago Style

Maffucci, R. 2019. “Nodal Intersections for Arithmetic Random Waves against a Surface.” Annales Henri Poincare 20 (1): 3651–91.
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Files:: Maffucci Nodal intersections.pdf

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Publisher copy:: 10.1007/s00023-019-00831-1

Authors

+ Maffucci, R More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Role:: Author

+ Engineering & Physical Sciences Research Council More from this funder

Grant:: EP/M002896/1

Publisher:: Springer
Journal:: Annales Henri Poincare More from this journal
Volume:: 20
Issue:: 1
Pages:: 3651-3691
Publication date:: 2019-08-08
Acceptance date:: 2019-07-23
DOI:: 10.1007/s00023-019-00831-1
EISSN:: 1424-0661
ISSN:: 1424-0637

Keywords:: FFR
Pubs id:: pubs:1038653
UUID:: uuid:d8f6e7b4-2197-4f7f-9e9d-812892fa1ec6
Local pid:: pubs:1038653
Source identifiers:: 1038653
Deposit date:: 2019-08-05

Terms of use

Copyright holder:: Maffucci
Copyright date:: 2019
Notes:: © The Author 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Licence:: CC Attribution (CC BY)

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