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Smoothing Operators in Multi-Marginal Optimal Transport
Mathematical Physics, Analysis and Geometry ( IF 1 ) Pub Date : 2020-05-28 , DOI: 10.1007/s11040-020-09349-z
Ugo Bindini

Given N absolutely continuous probabilities ρ 1 , … , ρ N $\rho _{1}, \dotsc , \rho _{N}$ over ℝ d ${\mathbb {R}}^{d}$ which have Sobolev regularity, and given a transport plan P with marginals ρ 1 , … , ρ N $\rho _{1}, \dotsc , \rho _{N}$ , we provide a universal technique to approximate P with Sobolev regular transport plans with the same marginals. Moreover, we prove a sharp control of the energy and some continuity properties of the approximating family.

中文翻译:

多边际最优传输中的平滑算子

给定 N 个绝对连续概率 ρ 1 , … , ρ N $\rho _{1}, \dotsc , \rho _{N}$ over ℝ d ${\mathbb {R}}^{d}$ 具有 Sobolev 规律,并给定一个具有边际 ρ 1 , … , ρ N $\rho _{1}, \dotsc , \rho _{N}$ 的交通计划 P,我们提供了一种通用技术来近似 P 与 Sobolev 常规交通计划相同的边缘。此外,我们证明了近似族的能量和一些连续性特性的严格控制。
更新日期:2020-05-28
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