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Convexity inequalities and optimal transport of infinite-dimensional measures

✍ Scribed by Alexander V. Kolesnikov

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
259 KB
Volume
83
Category
Article
ISSN
0021-7824

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✦ Synopsis

We generalize Talagrand's inequality in the theory of optimal transport and give some applications of our result. In particular, we establish an estimate for a couple of transportation mappings. In the finite-dimensional case we obtain a new log-Sobolev type inequality. In the infinite-dimensional case we consider transformations of measures absolutely continuous with respect to a given Gaussian measure.

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Convexity conditions of Kantorovich func
Convexity conditions of Kantorovich function and related semi-infinite linear matrix inequalities
✍ Yun-Bin Zhao πŸ“‚ Article πŸ“… 2011 πŸ› Elsevier Science 🌐 English βš– 289 KB

The Kantorovich function (x T Ax)(x T A -1 x), where A is a positive definite matrix, is not convex in general. From a matrix or convex analysis point of view, it is interesting to address the question: when is this function convex? In this paper, we prove that the 2-dimensional Kantorovich function