TY - JOUR

T1 - Complexity of Gaussian Random Fields with Isotropic Increments

AU - Auffinger, Antonio

AU - Zeng, Qiang

N1 - Funding Information:
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.
Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2023/8

Y1 - 2023/8

N2 - 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.

AB - 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.

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U2 - 10.1007/s00220-023-04739-0

DO - 10.1007/s00220-023-04739-0

M3 - Article

AN - SCOPUS:85163765083

SN - 0010-3616

VL - 402

SP - 951

EP - 993

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 1

ER -