A grid-sketching technique enables ε-accurate estimation of W₂² between α-Hölder smooth distributions on (0,1)^d in time ε^{-max(2, (d+1+o(1))/(1+α))}.
arXiv preprint arXiv:2507.05395 , year=
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Constructs solutions to Monge-Ampère equations with singular measures on low-codimensional sets, studies their regularity, and motivates the work with optimal transport examples.
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Optimizing Computational-Statistical Runtime for Wasserstein Distance Estimation
A grid-sketching technique enables ε-accurate estimation of W₂² between α-Hölder smooth distributions on (0,1)^d in time ε^{-max(2, (d+1+o(1))/(1+α))}.
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Solutions to Monge-Amp\`ere Equations with Low Codimensional singularities
Constructs solutions to Monge-Ampère equations with singular measures on low-codimensional sets, studies their regularity, and motivates the work with optimal transport examples.