Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4668979 | Bulletin des Sciences Mathématiques | 2011 | 12 Pages |
Abstract
For each Lp-Wasserstein distance (p>1) with the cost function induced by the L2-distance on loop groups, we show that there exists a unique optimal transport map solving the Monge–Kantorovich problem when the initial probability measure is absolutely continuous with respect to the heat kernel measure. In particular, this provides us a family of measurable maps on loop groups which push the heat kernel measure forward to the pinned Wiener measure.
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