Guy Bouchitte, Universite de Toulon
"Some asyptotic problems in optimal transportation"
We consider the optimal transport (in the
sense of the Monge-Kantorovich distance , ) of a given
) to an unknown
discrete measure . Our aim is to find the asymptotic as of
where is some energy on atomic measures. The case where is the number of points in the support of 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 plays a major role and allows us to solve the problem in a lot of other situations.
TUESDAY, April 22, 2003