paper
A quantitative stability result for the Prékopa-Leindler inequality for arbitrary measurable functions
Károly J. Böröczky, Alessio Figalli, João P. G. Ramos
A quantitative stability result for the Prékopa-Leindler inequality for arbitrary measurable functions
Károly J. Böröczky, Alessio Figalli, João P. G. Ramos
Paper2022-01-27English
quantitative financearxiv
Description
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.
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