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On the finiteness of the second moment of the number of critical points of Gaussian random fields
Samuel Davenport, Fabian J. E. Telschow · 2022-01-05 · via math.PR updates on arXiv.org

We prove that the second moment of the number of critical points of any sufficiently regular random field, for example with almost surely $ C^3 $ sample paths, defined over a compact Whitney stratified manifold is finite. Our results hold without the assumption of stationarity - which has traditionally been assumed in other work. Under stationarity we demonstrate that our imposed conditions imply the generalized Geman condition of Estrade 2016.

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