On critical points of Gaussian random fields under diffeomorphic transformations

Dan Cheng and Armin Schwartzman

Statistics & Probability Letters, 2020, vol. 158, issue C

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.

Keywords: Diffeomorphic transformation; Critical points; Expected number; Height distribution; Anisotropic; Isotropic (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2019.108672

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