Abstract for the talk at 17.04.2012 (15:15 h)

Oberseminar ANALYSIS
Karl-Theodor Sturm (Universität Bonn)
Optimal Transport from Lebesgue to Poisson
We study couplings qω of the Lebesgue measure 𝔏d and the Poisson point process μω on d. We ask for a minimizer of the mean Lp-transportation cost. The minimal mean Lp-transportation cost turns out to be finite for all p (0,) provided d 3. If d 2 then it is finite if and only if p < d∕2.

Moreover, in any of these cases we prove that there exist a unique translation invariant coupling which minimizes the mean Lp-transportation cost. In the case p = 2, this ’optimal coupling’ induces a random tiling of d by convex polytopes of volume 1.


01.03.2017, 13:57