An Explicit Bound on the Transportation Cost Distance

Abstract

We give what appears to be the first explicit, easily computable bound on the transportation cost distance with respect to the weighted Hamming metric. The bound follows from Kantorovich duality and a novel inequality, which amounts to bounding the maximal value of certain linear programs and may be of independent interest. We give two application to concentration of measure for dependent processes and pose some open problems and directions for future work.