Calculus of the coarse Ricci curvatures κ and ˜κ on an example of degenerated diffusion
Résumé
The use of classical tools like the Bakry-Emery curvature can fail to provide functional inequalities in the case of degenerated diffusions. This is the case in the example we study here. However, the use of Ollivier's coarse Ricci curvature used with a diferent metric than the one canonically associated with the diffusion allows to get a Poincaré inequality (with a non optimal constant nonetheless).
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