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math.AP2024
Optimal transport maps, majorization, and log-subharmonic measures
Guido De Philippis, Yair Shenfeld
Caffarelli's contraction theorem bounds the derivative of the optimal transport map between a log-convex measure and a strongly log-concave measure. We show that an analogous pheno…
math.AP2023
Matrix displacement convexity along density flows
Yair Shenfeld
A new notion of displacement convexity on a matrix level is developed for density flows arising from mean-field games, compressible Euler equations, entropic interpolation, and sem…