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The Gaussian Free Field (GFF) of dimension d is a gaussian stochastic process $(X_v, v \in B_N)$ where the variables are indexed by the vertices of a box $B_N \in \mathbb{Z}^d$. The covariance matrix is given by the Green's function of the discrete Laplace operator on $B_N$ with Dirichlet boundary conditions.

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Q: What is the distribution of the maxima of the Gaussian free field for dimensions higher than or equal to three?
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