$W_{1,+}$ -图上概率测度的插值
$W_{1,+}$-interpolation of probability measures on graphs
摘要：
本文将Benamou和Brenier引入的刻画Wasserstein W_p-测地线（p > 1）的方程从黎曼流形上概率分布的连续设置推广到一般图上概率分布的离散设置.给定初始和最终分布f_0和f_1，我们证明了满足Benamou-Brenier方程的曲线（f_t）的存在性。我们还表明，这样的曲线可以被描述为一个混合物的二项分布相对于一个耦合，这是解决一定的最优化问题。
英文摘要：
We generalize an equation introduced by Benamou and Brenier, characterizing Wasserstein W_p-geodesics for p > 1, from the continuous setting of probability distributions on a Riemannian manifold to the discrete setting of probability distributions on a general graph. Given an initial and a final distributions f_0 and f_1, we prove the existence of a curve (f_t) satisfying this Benamou-Brenier equation. We also show that such a curve can be described as a mixture of binomial distributions with respect to a coupling that is solution of a certain optimization problem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
