# Complexity of Gaussian random fields with isotropic increments: critical points with given indices

@inproceedings{Auffinger2020ComplexityOG, title={Complexity of Gaussian random fields with isotropic increments: critical points with given indices}, author={Antonio Auffinger and Qiang Zeng}, year={2020} }

We study the landscape complexity of the Hamiltonian X N ( x )+ µ 2 k x k 2 , where X N is a smooth Gaussian process with isotropic increments on R N . This model describes a single particle on a random potential in statistical physics. We derive asymptotic formulas for the mean number of critical points of index k with critical values in an open set as the dimension N goes to inﬁnity. In a companion paper, we provide the same analysis without the index constraint.

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