## Fluctuations of the Nodal Line Length of Laplace eigenfunctions on the Arithmetic torus

ANALYSIS AND MATHEMATICAL PHYSICS SEMINAR

Using the spectral multiplicities of the standard torus, we endow the Laplace eigenspace with Gaussian probability measure. This induces a notion of a random Gaussian Laplace eigenfunctions on the torus. We study the distribution of nodal length of the random Laplace eigenfunctions for high eigenvalues ("high energy limit").