A quantitative stability result for the Prékopa–Leindler inequality for arbitrary measurable functions

A quantitative stability result for the Prékopa–Leindler inequality for arbitrary measurable functions

We prove that if a triplet of functions satisfies almost-equality in the Prékopa–Leindler inequality, then these functions are close to a common log-concave function, up to multiplication and rescaling. Our result holds for general measurable functions in all dimensions, and provides a quantitative...

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Veröffentlicht in:Annales de l'Institut Henri Poincaré. Analyse non linéaire 2024-05, Vol.41 (3), p.565-614
Hauptverfasser: Böröczky, Károly J., Figalli, Alessio, Ramos, João P. G.
Format: Artikel
Sprache:eng
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Zusammenfassung:We prove that if a triplet of functions satisfies almost-equality in the Prékopa–Leindler inequality, then these functions are close to a common log-concave function, up to multiplication and rescaling. Our result holds for general measurable functions in all dimensions, and provides a quantitative stability estimate with computable constants.
ISSN:0294-1449
1873-1430
DOI:10.4171/aihpc/97