Quantitative Harris type theorems for diffusions and McKean-Vlasov processes

Understand

We consider $\mathbb{R}^d$-valued diffusion processes of type \begin{align*} dX_t\ =\ b(X_t)dt\, +\, dB_t.

• \end{align*} Assuming a geometric drift condition, we establish contractions of the transitions kernels in Kantorovich ($L^1$ Wasserstein) distances with explicit constants.
• Our results are in the spirit of Hairer and Mattingly's extension of Harris' Theorem.
• In particular, they do not rely on a small set condition.