On critical points of Gaussian random fields under diffeomorphic transformations

Dan Cheng, Armin Schwartzman

Research output: Contribution to journalArticlepeer-review


Let {X(t),t∈M} and {Z(t),t∈M} be smooth Gaussian random fields parameterized on Riemannian manifolds M and M, respectively, such that X(t)=Z(f(t)), where f:M→M is a diffeomorphic transformation. We study the expected number and height distribution of the critical points of X in connection with those of Z. As an important case, when X is an anisotropic Gaussian random field, then we show that its expected number of critical points becomes proportional to that of an isotropic field Z, while the height distribution remains the same as that of Z.

Original languageEnglish (US)
Article number108672
JournalStatistics and Probability Letters
StatePublished - Mar 2020


  • Anisotropic
  • Critical points
  • Diffeomorphic transformation
  • Expected number
  • Height distribution
  • Isotropic

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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