Complexity of Gaussian Random Fields with Isotropic Increments

Antonio Auffinger*, Qiang Zeng

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)951-993
Number of pages43
JournalCommunications in Mathematical Physics
Issue number1
StatePublished - Aug 2023

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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