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Optimal transport for multifractal random measures. Applications
Random measures multifractal processes optimal transport metric KPZ
2010/11/26
In this paper, we study optimal transportation problems for multifractal random measures. Since these measures are much less regular than optimal transportation theory requires, we introduce a new not...
Ricci curvature, entropy and optimal transport
Ricci curvature entropy optimal transport curvature-dimension condition
2010/12/8
This is the lecture notes on the interplay between optimal transport and Riemannian geometry. On a Riemannian manifold, the convexity of entropy along optimal transport in the space of probability mea...
Lecture Notes on Gradient Flows and Optimal Transport
Lecture Notes Gradient Flows Optimal Transport
2010/12/9
We present a short overview on the strongest variational formulation for gradient flows of geodesically -convex functionals in metric spaces, with applications to diffusion equations in Wasserstein s...