Carnegie Mellon
Department of Mathematical 

Guy Bouchitte, Universite de Toulon

"Some asyptotic problems in optimal transportation"


We consider the optimal transport (in the sense of the Monge-Kantorovich distance $W_p$, $p\ge 1$) of a given density $f\in L^1(\Omega)$ ( $\Omega \subset R^d$) to an unknown discrete measure $\nu$. Our aim is to find the asymptotic as $m\to
\infty$ of

\begin{displaymath}\inf\{ W_p(f,\nu) \ :\ G(\nu) \le m \} \ ,\end{displaymath}

where $G$ is some energy on atomic measures. The case where $G(\nu)$ is the number of points in the support of $\nu$ corresponds to an optimal location problem which has been considered in economy (optimal location of production centers) or in information theory (quantization of random variables). We will show how the the case $G(\nu):= \sum \nu(
\{x\})^{1+{p\over d}}$ plays a major role and allows us to solve the problem in a lot of other situations.

TUESDAY, April 22, 2003
Time: 1:30 P.M.
Location: PPB 300