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Wasserstein asymptotics for empirical measures of diffusions on four dimensional closed manifolds
Dario Trevisan, Feng-Yu Wang, Jie-Xiang Zhu
We identify the leading term in the asymptotics of the quadratic Wasserstein distance between the invariant measure and empirical measures for diffusion processes on closed weighte…
Asymptotics for Random Quadratic Transportation Costs
Martin Huesmann, Michael Goldman, Dario Trevisan
We establish the validity of asymptotic limits for the general transportation problem between random i.i.d. points and their common distribution, with respect to the squared Euclid…
Subadditivity and optimal matching of unbounded samples
Emanuele Caglioti, Michael Goldman, Francesca Pieroni +1
We obtain new bounds for the optimal matching cost for empirical measures with unbounded support. For a large class of radially symmetric and rapidly decaying probability laws, we…
Quantitative stability in optimal transport for general power costs
Octave Mischler, Dario Trevisan
We establish novel quantitative stability results for optimal transport problems with respect to perturbations in the target measure. We provide explicit bounds on the stability of…
Sharp PDE estimates for random two-dimensional bipartite matching with power cost function
Luigi Ambrosio, Federico Vitillaro, Dario Trevisan
We investigate the random bipartite optimal matching problem on a flat torus in two-dimensions, considering general strictly convex power costs of the distance. We extend the succe…