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Let $\\Delta$ be the Laplacian on ${\\mathcal{X}}$, and let $(e\\_k)\\_k$ be an $L^2$-orthonormal and dense family of Laplace eigenfunctions with respective eigenvalues  $(\\lambda\\_k)\\_k$. We assume that $(\\lambda\\_k)\\_k$ is non-decreasing and that the $e\\_k$ are real-valued. Let $(\\xi\\_k)\\_k$ be a sequence of iid $\\mathcal{N}(0,1)$ random variables. 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