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arXiv · 2408.14383

A law of large numbers concerning the number of critical points of isotropic Gaussian functions

Liviu I. Nicolaescu
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Abstract

We investigate the distribution of critical points of certain isotropic random functions $\Phi$ on $\mathbb{R}^m$. We show that the distribution of critical points of $\Phi(Rx)$, 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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Liviu I. Nicolaescu. 2024-08-26. A law of large numbers concerning the number of critical points of isotropic Gaussian functions. https://arxiv.org/abs/2408.14383

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