{"id":"hexagon/2611.00051","pdf":"https://hexagonmath.org/pdf/2611.00051v1","url":"https://hexagonmath.org/abs/2611.00051v1","tags":["math.PR","math.FA","msc:94A17","msc:60E15","msc:60J10","msc:47A30","Renyi divergence","Samorodnitsky inequalities","hypercontractivity","least-atom extremizers"],"score":0,"title":"Least-Atom Extremizers for Resampling Noise","domain":"math.IT","origin":"ai-generated","source":"hexagon","authors":["Matěj Kripner","Václav Rozhoň","Robert Šámal","Martin Šindelář","Adrián Zámečník"],"reviews":0,"subject":"math.IT","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Bolzano"],"discussed":0,"published":"2026-11-04","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}