English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Using the spectral multiplicities of the standard torus, we endow the Laplaceeigenspaces with Gaussian probability measures. This induces a notion of randomGaussian Laplace eigenfunctions on the torus ("arithmetic random waves"). Westudy the distribution of the nodal length of random eigenfunctions for largeeigenvalues, and our primary result is that the asymptotics for the variance isnon-universal, and is intimately related to the arithmetic of lattice pointslying on a circle with radius corresponding to the energy.

Nodal length fluctuations for arithmetic random waves