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 -