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Wasserstein diffusion on multidimensional spaces

Karl-Theodor Sturm

Annals of Probability2026https://doi.org/10.1214/25-aop1774article
ABDC A*
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0.50

Abstract

Given any closed Riemannian manifold M, we construct a stochastic perturbation of the heat flow as a continuous Markov process on the space P(M) of probability measures on M, that is: (1) reversible w.r.t. the entropic measure Pβ on P(M), heuristically given as dPβ(μ)=1 Ze−βEnt(μ|m)dP∗(μ); (2) associated with a regular Dirichlet form with carré du champ derived from the Wasserstein gradient in the sense of Otto calculus EW(f)=lim infg→f 1 2∫P(M)‖∇Wg‖2(μ)dPβ(μ); (3) nondegenerate, at least in the case of the n-sphere and the n-torus. And yet it moves. Galileo Galilei, 1633

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https://doi.org/https://doi.org/10.1214/25-aop1774

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@article{karl-theodor2026,
  title        = {{Wasserstein diffusion on multidimensional spaces}},
  author       = {Karl-Theodor Sturm},
  journal      = {Annals of Probability},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1214/25-aop1774},
}

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Wasserstein diffusion on multidimensional spaces

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Evidence weight

0.50

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.50 × 0.4 = 0.20
M · momentum0.50 × 0.15 = 0.07
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

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