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Current open questions in complete mixability. (English) Zbl 1328.60023

Summary: Complete and joint mixability has raised considerable interest in recent few years, in both the theory of distributions with given margins, and applications in discrete optimization and quantitative risk management. We list various open questions in the theory of complete and joint mixability, which are mathematically concrete, and yet accessible to a broad range of researchers without specific background knowledge. In addition to the discussions on open questions, some results contained in this paper are new.

MSC:

60C05 Combinatorial probability
60E05 Probability distributions: general theory
60E15 Inequalities; stochastic orderings
60-02 Research exposition (monographs, survey articles) pertaining to probability theory
00A07 Problem books

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