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An entropic interpolation proof of the HWI inequality (1807.06893v1)
Published 18 Jul 2018 in math.PR and math.CA
Abstract: We present a pathwise proof of the HWI inequality which is based on en-tropic interpolations rather than displacement ones. Unlike the latter, entropic interpolations are regular both in space and time. Consequently, our approach is closer to the Otto-Villani heuristics, presented in the first part of the article [23], than the original rigorous proof presented in the second part of [23].