Add to ORKGFor a compact hyperbolic surface, we define a smooth linear statistic, mimicking the number of Laplace eigenvalues in a short energy window. We study the variance of this statistic, when averaged over the moduli space $\mathcal M_g$ of all genus $g$ surfaces with respect to the Weil-Petersson measure. We show that in the double limit, first taking the large genus limit and then the high energy limit, we recover GOE statistics. The proof makes essential use of Mirzakhani's integration formula.Comment: Added details and correction
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In this paper, we investigate basic geometric quantities of a random hyperbolic surface of genus $g$...
We study the high--energy limit for eigenfunctions of the laplacian, on a compact negatively curved ...
Random hyperspherical harmonics are Gaussian Laplace eigenfunctions on the unit $d$-dimensional sphe...
We give a quantitative estimate for the quantum mean absolute deviation on hyperbolic surfaces in te...
We study geometric and spectral properties of typical hyperbolic surfaces of high genus, excluding a...
The aim of thesis is to prove new results on the geometry and spectrum of typical compact hyperbolic...
We prove Poisson approximation results for the bottom part of the length spectrum of a random closed...
This paper studies the Weil-Petersson measure on the moduli space of compact hyperbolic surfaces of ...
We give upper bounds for Lp norms of eigenfunctions of the Laplacian on compact hyperbolic surfaces ...
We describe a new approach to understanding averages of high energy Laplace eigenfunctions, uh, over...
We prove that eigenfunctions of the Laplacian on a compact hyperbolic surface delocalise in terms of...
We consider quadratic forms of deterministic matrices $A$ evaluated at the random eigenvectors of a ...
Let $S_g$ be a closed surface of genus $g$ and $\mathbb{M}_g$ be the moduli space of $S_g$ endowed w...
In this paper, we determine the distribution of the length partition of a random multicurve of fixed...
We express the Masur-Veech volume and the area Siegel-Veech constant of the moduli space $\mathcal{Q...
In this paper, we investigate basic geometric quantities of a random hyperbolic surface of genus $g$...
We study the high--energy limit for eigenfunctions of the laplacian, on a compact negatively curved ...
Random hyperspherical harmonics are Gaussian Laplace eigenfunctions on the unit $d$-dimensional sphe...