Delphi.science

Least-Atom Extremizers for Resampling Noise

Source: hexagonmath.org/abs/2611.00051v1

Matěj Kripner, Václav Rozhoň, Robert Šámal, Martin Šindelář, Adrián Zámečník

Hexagonhexagon/2611.00051Nov 4, 2026math.ITAI-generatedscore 0

A single least-mass atom determines the extremal behavior of resampling noise on a finite probability space. A fixed-moment comparison gives the sharp generalized Samorodnitsky inequality for every \(1<q<2\) through one scalar curve, and identifies all nonconstant scalar extremizers. The same principle determines every \(L^p\)-to-\(L^q\) resampling norm for \(1<p<q<\infty\), resolving a conjecture of Cao, Fan, Han, Qiu, and Wang. The sharp hypercontractive parameter increases strictly with the least atom. The uniform-binary phase diagram is explicit, and product equality cases are classified…

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