A law of large numbers concerning the number of critical points of isotropic Gaussian functions
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909414673350656 |
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| author | Nicolaescu, Liviu I. |
| author_facet | Nicolaescu, Liviu I. |
| contents | 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 $R\to\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14383 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A law of large numbers concerning the number of critical points of isotropic Gaussian functions Nicolaescu, Liviu I. Probability Classical Analysis and ODEs 60F15, 60D05, 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 $R\to\infty$. |
| title | A law of large numbers concerning the number of critical points of isotropic Gaussian functions |
| topic | Probability Classical Analysis and ODEs 60F15, 60D05, |
| url | https://arxiv.org/abs/2408.14383 |