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A remark on discrete Brunn–Minkowski type inequalities via transportation of measure

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Abstract

We give an alternative proof for discrete Brunn–Minkowski type inequalities, recently obtained by Halikias, Klartag and the author. This proof also implies somewhat stronger weighted versions of these inequalities. Our approach generalizes ideas of Gozlan, Roberto, Samson and Tetali from the theory of measure transportation and provides new displacement convexity of entropy type inequalities on the n-dimensional integer lattice.

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Acknowledgements

I am grateful to Bo’az Klartag for fruitful conversions and for his advice and comments. I would like to thank Shiri Artstein and the anonymous referee for their useful remarks and suggestions. I would also like to thank the anonymous referee of the paper [10] for suggesting to pursue this direction of research. Supported by ISF grant 784/20.

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Authors and Affiliations

  1. Department of Mathematics, The Open University of Israel, Ra’anana, 4353701, Israel

    Boaz A. Slomka

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  1. Boaz A. Slomka
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Correspondence to Boaz A. Slomka.

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Slomka, B.A. A remark on discrete Brunn–Minkowski type inequalities via transportation of measure. Isr. J. Math. (2023). https://doi.org/10.1007/s11856-023-2596-3

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  • DOI: https://doi.org/10.1007/s11856-023-2596-3

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