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arXiv · 2007.07668

Complexity of Gaussian random fields with isotropic increments

Antonio Auffinger·Qiang Zeng
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Abstract

We study the energy landscape of a model of a single particle on a random potential, that is, we investigate the topology of level sets of smooth random fields on $\mathbb R^{N}$ of the form $X_N(x) +\frac\mu2 \|x\|^2,$ where $X_{N}$ is a Gaussian process with isotropic increments. We derive asymptotic formulas for the mean number of critical points with critical values in an open set as the dimension $N$ goes to infinity. In a companion paper, we provide the same analysis for the number of critical points with a given index.

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Antonio Auffinger, Qiang Zeng. 2020-07-15. Complexity of Gaussian random fields with isotropic increments. https://arxiv.org/abs/2007.07668

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