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A Monotone Approximation to the Wasserstein Diffusion

In: Singular Phenomena and Scaling in Mathematical Models

Author

Listed:
  • Karl-Theodor Sturm

    (Rheinische Friedrich-Wilhelms-Universität Bonn, Institut für Angewandte Mathematik)

Abstract

The Wasserstein space $$\mathcal{P}(M)$$ on an Euclidean or Riemannian space M – i.e. the space of probability measures on M equipped with the L 2-Wasserstein distance d W – offers a rich geometric structure. This allows to develop a far reaching first order calculus, with striking applications for instance to the reformulation of conservative PDEs on M as gradient flows of suitable functionals on $$\mathcal{P}(M)$$ , see e.g. [1, 7, 11].

Suggested Citation

  • Karl-Theodor Sturm, 2014. "A Monotone Approximation to the Wasserstein Diffusion," Springer Books, in: Michael Griebel (ed.), Singular Phenomena and Scaling in Mathematical Models, edition 127, pages 25-48, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-00786-1_2
    DOI: 10.1007/978-3-319-00786-1_2
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