Random eigenfunctions on flat tori: universality for the number of intersections

TL;DR

This paper demonstrates that the statistical behavior of the number of intersections between random eigenfunctions and smooth curves on flat tori is universal across different types of randomness, indicating a broad applicability of these results.

Contribution

It establishes universality results for intersection statistics of random eigenfunctions on flat tori across various random models.

Findings

Statistics are universal under different randomness models.

Results apply to general eigenvalues and smooth curves.

Supports broader applicability of eigenfunction intersection behavior.

Abstract

We show that several statistics of the number of intersections between random eigenfunctions of general eigenvalues with a given smooth curve in flat tori are universal under various families of randomness.