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A law of large numbers concerning the number of critical points of isotropic Gaussian functions
Liviu I. Nicolaescu · 2024-08-27 · via math.PR updates on arXiv.org

We investigate the distribution of critical points of certain isotropic random functions $Φ$ on $\mathbb{R}^m$. We show that the distribution of critical points of $Φ(Rx)$, suitably normalized, converge a.s. and $L^2$ as random measures to the (deterministic) Lebesgue measure as $R\to\infty$. We achieve this by producing precise asymptotics of the second moments of these distributions as $R\to\infty$.

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