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.

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

UR - http://www.scopus.com/inward/record.url?scp=85075264165&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85075264165&partnerID=8YFLogxK

U2 - 10.1016/j.spl.2019.108672

DO - 10.1016/j.spl.2019.108672

M3 - Article

AN - SCOPUS:85075264165

VL - 158

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

M1 - 108672

ER -