Ricci curvature of Markov chains on metric spaces

@article{Ollivier2007RicciCO,
  title={Ricci curvature of Markov chains on metric spaces},
  author={Yann Ollivier},
  journal={Journal of Functional Analysis},
  year={2007},
  volume={256},
  pages={810-864}
}
  • Y. Ollivier
  • Published 2007
  • Mathematics
  • Journal of Functional Analysis
Abstract We define the coarse Ricci curvature of metric spaces in terms of how much small balls are closer (in Wasserstein transportation distance) than their centers are. This definition naturally extends to any Markov chain on a metric space. For a Riemannian manifold this gives back, after scaling, the value of Ricci curvature of a tangent vector. Examples of positively curved spaces for this definition include the discrete cube and discrete versions of the Ornstein–Uhlenbeck process… Expand
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