Improved Stability Versions of the Prékopa-Leindler Inequality
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Date
2025-02
Publication Type
Journal Article
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yes
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Abstract
We consider the problem of stability for the Prékopa-Leindler inequality. Exploiting properties of the transport map between radially decreasing functions and a suitable functional version of the trace inequality, we obtain a uniform stability exponent for the Prékopa-Leindler inequality. Our result yields an exponent not only uniform in the dimension but also in the log-concavity parameter τ = min(λ, 1- λ) associated with its respective version of the Prékopa-Leindler inequality. As a further application of our methods, we prove a sharp stability result for log-concave functions in dimension 1, which also extends to a sharp stability result for log-concave radial functions in higher dimensions.
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published
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Journal / series
Volume
32 (1)
Pages / Article No.
291 - 320
Publisher
Heldermann Verlag
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Subject
Prekopa-Leindler; stability; log-concavity
Organisational unit
09565 - Figalli, Alessio / Figalli, Alessio