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- W3191991544 abstract "We study the correlation between the total number of critical points of random spherical harmonics and the number of critical points with value in any interval <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper I subset-of double-struck upper R> <mml:semantics> <mml:mrow> <mml:mi>I</mml:mi> <mml:mo>⊂<!-- ⊂ --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>R</mml:mi> </mml:mrow> </mml:mrow> <mml:annotation encoding=application/x-tex>I subset mathbb {R}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We show that the correlation is asymptotically zero, while the partial correlation, after controlling the random <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper L squared> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:annotation encoding=application/x-tex>L^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-norm on the sphere of the eigenfunctions, is asymptotically one. Our findings complement the results obtained by Wigman (2012) and Marinucci and Rossi (2021) on the correlation between nodal and boundary length of random spherical harmonics." @default.
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- W3191991544 date "2022-05-16" @default.
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- W3191991544 title "On the correlation between critical points and critical values for random spherical harmonics" @default.
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- W3191991544 doi "https://doi.org/10.1090/tpms/1164" @default.
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