Joint Mixability
研究了给定边际分布下随机变量之和的可能分布，提出联合可混合性概念，给出均匀分布等几类分布联合可混合的充要条件，对风险聚合和概率不等式优化有应用。
Many optimization problems in probabilistic combinatorics and mass transportation impose fixed marginal constraints. A natural and open question in this field is to determine all possible distributions of the sum of random variables with given marginal distributions; the notion of joint mixability is introduced to address this question. A tuple of univariate distributions is said to be jointly mixable if there exist random variables, with respective distributions, such that their sum is a constant. We obtain necessary and sufficient conditions for the joint mixability of some classes of distributions, including uniform distributions, distributions with monotone densities, distributions with unimodal-symmetric densities, and elliptical distributions with the same characteristic generator. Joint mixability is directly connected to many open questions on the optimization of convex functions and probabilistic inequalities with marginal constraints. The results obtained in this paper can be applied to find extreme scenarios on risk aggregation under model uncertainty at the level of dependence.