Hole probability for nodal sets of the cut-off Gaussian Free Field

@inproceedings{Rivera2016HolePF,
title={Hole probability for nodal sets of the cut-off Gaussian Free Field},
author={Alejandro Rivera},
year={2016}
}
Let ($\Sigma$, g) be a closed connected surface equipped with a riemannian metric. Let ($\lambda$ n) n$\in$N and ($\psi$ n) n$\in$N be the increasing sequence of eigenvalues and the sequence of corresponding L 2-normalized eigenfunctions of the laplacian on $\Sigma$. For each L \textgreater{} 0, we consider $\phi$ L = 0\textless{}$\lambda$n$\le$L $\xi$n $\sqrt$ $\lambda$n $\psi$ n where the $\xi$ n are i.i.d centered gaussians with variance 1. As L $\rightarrow$ $\infty$, $\phi$ L converges a.s… CONTINUE READING
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