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- W4313495251 abstract "In this paper, we show that the set of random points uniformly distributed over <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=double-struck upper S Superscript n minus 1> <mml:semantics> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>S</mml:mi> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>n</mml:mi> <mml:mo>โ<!-- โ --></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:annotation encoding=application/x-tex>mathbb {S}^{n-1}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a stable set of sampling for a class of localized functions in <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper L squared left-parenthesis double-struck upper S Superscript n minus 1 Baseline right-parenthesis> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo stretchy=false>(</mml:mo> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>S</mml:mi> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>n</mml:mi> <mml:mo>โ<!-- โ --></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>L^2(mathbb {S}^{n-1})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with overwhelming probability. The probability bound of the random sampling inequality for the localized function is obtained from the matrix Bernstein inequality on the independent random matrices." @default.
- W4313495251 created "2023-01-06" @default.
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- W4313495251 date "2023-06-23" @default.
- W4313495251 modified "2023-09-26" @default.
- W4313495251 title "Spherical random sampling of localized functions on ๐โฟโปยน" @default.
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- W4313495251 doi "https://doi.org/10.1090/proc/16393" @default.
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