The HWI inequality is an "interpolation" inequality between the Entropy H, the Fisher information I and the Wasserstein distance W. We present a pathwise proof of the HWI inequality which is obtained through a zero noise limit of the Schrodinger problem. Our approach consists in making rigorous the Otto-Villani heuristics in Otto and Villani (2000) taking advantage of the entropic interpolations, which are regular both in space and time, rather than the displacement ones.
Gentil, I., Leonard, C., Ripani, L., Tamanini, L., An entropic interpolation proof of the HWI inequality, <<STOCHASTIC PROCESSES AND THEIR APPLICATIONS>>, 2020; 130 (2): 907-923. [doi:10.1016/j.spa.2019.04.002] [https://hdl.handle.net/10807/232496]
An entropic interpolation proof of the HWI inequality
Tamanini, Luca
2020
Abstract
The HWI inequality is an "interpolation" inequality between the Entropy H, the Fisher information I and the Wasserstein distance W. We present a pathwise proof of the HWI inequality which is obtained through a zero noise limit of the Schrodinger problem. Our approach consists in making rigorous the Otto-Villani heuristics in Otto and Villani (2000) taking advantage of the entropic interpolations, which are regular both in space and time, rather than the displacement ones.
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