A central limit theorem for the Euler characteristic of a Gaussian excursion set

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A quantitative central limit theorem for the Euler–Poincaré characteristic of random spherical eigenfunctions (2016, methodology): “It is then convenient to implement a linear transform on this vector, to make its components independent when evaluated on the same point x ∈ S2; this idea is analogous to the approach which was pursue by [14] in their recent work on the Euler–Poincaré characteristic for Gaussian field on an Euclide”