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.

中文翻译：

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通过测度传输对离散 Brunn-Minkowski 型不等式的评论

我们给出了离散 Brunn-Minkowski 型不等式的另一种证明，该证明最近由 Halikias、Klartag 和作者获得。这个证明还暗示了这些不等式的更强的加权版本。我们的方法从测度传输理论中概括了 Gozlan、Roberto、Samson 和 Tetali 的思想，并提供了n维整数格上熵型不等式的新位移凸性。