### Abstract

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 language | English (US) |
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Article number | 108672 |

Journal | Statistics and Probability Letters |

Volume | 158 |

DOIs | |

State | Published - Mar 2020 |

Externally published | Yes |

### Keywords

- 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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## Cite this

Cheng, D., & Schwartzman, A. (2020). On critical points of Gaussian random fields under diffeomorphic transformations.

*Statistics and Probability Letters*,*158*, [108672]. https://doi.org/10.1016/j.spl.2019.108672