2 problems

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Equality of boundary and bulk optimal matching constants
Let $X_1,X_2,\ldots$ be independent random variables uniformly distributed on the unit cube $Q=(0,1)^d$ , let $\mu_n=\sum_{i=1}^n\delta_{X_i}$ , and define … Set … and … where…
Conjectureopenoptimal-matching optimal-transport wasserstein-distancearXiv posted 2 days ago
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Caracciolo–Lucià–Parisi–Sicuro conjecture for two-dimensional optimal matching
Caracciolo–Lucià–Parisi–Sicuro conjecture. The renormalized expected cost has a finite limit:
Conjectureopenoptimal-matching optimal-transport wasserstein-distancearXiv posted 2 days ago

Equality of boundary and bulk optimal matching constants