Random waves on T3: Nodal area variance and lattice point correlations

Jacques Benatar, Riccardo W. Maffucci*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider the ensemble of random Gaussian Laplace eigenfunctions on T3 = R3/Z3 ("3 dimensional arithmetic random waves"), and study the distribution of their nodal surface area. The expected area is proportional to the square root of the eigenvalue, or "energy", of the eigenfunction. We show that the nodal area variance obeys an asymptotic law. The resulting asymptotic formula is closely related to the angular distribution and correlations of lattice points lying on spheres.

Original languageEnglish
Article numberrnx220
Pages (from-to)3032-3075
Number of pages44
JournalInternational Mathematics Research Notices
Issue number10
StatePublished - 17 May 2019
Externally publishedYes


Dive into the research topics of 'Random waves on T3: Nodal area variance and lattice point correlations'. Together they form a unique fingerprint.

Cite this