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On critical points of Gaussian random fields under diffeomorphic transformations

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  • Cheng, Dan
  • Schwartzman, Armin

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.

Suggested Citation

  • Cheng, Dan & Schwartzman, Armin, 2020. "On critical points of Gaussian random fields under diffeomorphic transformations," Statistics & Probability Letters, Elsevier, vol. 158(C).
    • Handle: RePEc:eee:stapro:v:158:y:2020:i:c:s0167715219303189
    DOI: 10.1016/j.spl.2019.108672
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    References listed on IDEAS

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    1. Taylor, Jonathan E. & Worsley, Keith J., 2007. "Detecting Sparse Signals in Random Fields, With an Application to Brain Mapping," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 913-928, September.
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