ERC Workshop on Optimal Transportation and Applications
timetable:
Tue 6 Nov, 14:30 - 15:00, Aula Dini
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From Knothe's Rearrangement to Brenier's Map
speaker: Nicolas Bonnotte (Université Paris-Sud, Scuola Normale Superiore)abstract: The aim of this talk is to show how the Kantorovich potential for Brenier's map can be obtained as the value at time \(t = 1\) of the solution of a Cauchy problem, constisting of a PDE and a strange initial value for \(t = 0\), which corresponds to the Knothe-Rosenblatt rearragement. In fact, the value at time \(t\) of this solution is nothing but the potential for the cost \(c(x,y) = |x_1-y_1|^2 + t\cdot|x_2-y_2|^2 +\ldots+ t^{d-1}\cdot|x_d-y_d|^2\).
timetable:
Tue 6 Nov, 14:30 - 15:00, Aula Dini
<< Go back