Distance riemannienne, théorème de Rademacher et inégalité de transport sur le groupe des lacets

In this Note, we shall consider the Riemannian distance on loop groups, which will be identified to one introduced by Hino and Ramirez [M. Hino, J.A. Ramirez, Small-time Gaussian behavior of symmetric diffusion semigroups, Ann. Probab. 31 (2003) 1254-1295]. A transportation cost inequality is established. To cite this article: S. Fang, J. Shao, C. R. Acad. Sci. Paris, Ser. I 341 (2005).