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 RN of the form XN(x)+μ2‖x‖2, where XN 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.
Original language | English (US) |
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Pages (from-to) | 951-993 |
Number of pages | 43 |
Journal | Communications in Mathematical Physics |
Volume | 402 |
Issue number | 1 |
DOIs | |
State | Published - Aug 2023 |
Funding
Antonio Auffinger: research partially supported by NSF Grant CAREER DMS-1653552 and NSF Grant DMS-1517894. Qiang Zeng: research partially supported by SRG 2020-00029-FST and FDCT 0132/2020/A3.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics