• Corpus ID: 246035950

Wasserstein contraction and Poincar\'e inequalities for elliptic diffusions at high temperature

@inproceedings{Monmarche2022WassersteinCA,
  title={Wasserstein contraction and Poincar\'e inequalities for elliptic diffusions at high temperature},
  author={Pierre Monmarch'e},
  year={2022}
}
We consider elliptic diffusion processes on Rd. Assuming that the drift contracts distances outside a compact set, we prove that, at a sufficiently high temperature, the Markov semi-group associated to the process is a contraction of the W2 Wasserstein distance, which implies a Poincaré inequality for its invariant measure. The result doesn’t require neither reversibility nor an explicit expression of the invariant measure, and the estimates have a sharp dependency on the dimension. Some… 

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