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Complexity Function of Isotropic Gaussian Random Fields
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DOI：10.1007/s10959-026-01491-8.png)
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Abstract
En 中文
We study the landscape complexity of the Hamiltonian X-N (x) + mu/2 ||x ||(2), where mu > 0 and X-N is an isotropic Gaussian random field on R-N. We derive asymptotic formulas for the expected number of critical points of the Hamiltonian, as the dimension N tends to infinity. These results complement the corresponding findings for locally isotropic Gaussian random fields, as well as the work of Auffinger and Zeng (Auffinger and Zeng 402:951-9932023, 2022) on non-isotropic Gaussian random fields with isotropic increments.
Keywords:
Isotropic Gaussian fields
Critical points
Kac-Rice formula
Landscape complexity
Journal
J
IF:
0.6
Papers:
64
Citations:
0