TY - JOUR
T1 - On critical points of Gaussian random fields under diffeomorphic transformations
AU - Cheng, Dan
AU - Schwartzman, Armin
N1 - Funding Information:
Research partially supported by National Science Foundation, USA grant DMS-1902432.Research partially supported by National Science Foundation, USA grant DMS-1811659.
Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2020/3
Y1 - 2020/3
N2 - 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.
AB - 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.
KW - Anisotropic
KW - Critical points
KW - Diffeomorphic transformation
KW - Expected number
KW - Height distribution
KW - Isotropic
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U2 - 10.1016/j.spl.2019.108672
DO - 10.1016/j.spl.2019.108672
M3 - Article
AN - SCOPUS:85075264165
SN - 0167-7152
VL - 158
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
M1 - 108672
ER -