English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $P_t$ be the (Neumann) diffusion semigroup $P_t$ generated by a weightedLaplacian on a complete connected Riemannian manifold $M$ without boundary orwith a convex boundary. It is well known that the Bakry-Emery curvature isbounded below by a positive constant $\ll>0$ if and only if $$W_p(\mu_1P_t,\mu_2P_t)\le \e^{-\ll t} W_p (\mu_1,\mu_2),\ \ t\ge 0, p\ge 1 $$ holds for allprobability measures $\mu_1$ and $\mu_2$ on $M$, where $W_p$ is the $L^p$Wasserstein distance induced by the Riemannian distance. In this paper, weprove the exponential contraction $$W_p(\mu_1P_t, \mu_2P_t)\le c\e^{-\ll t} W_p(\mu_1,\mu_2),\ \ p\ge 1, t\ge 0$$ for some constants $c,\ll>0$ for a class ofdiffusion semigroups with negative curvature where the constant $c$ isessentially larger than $1$. Similar results are derived for SDEs withmultiplicative noise by using explicit conditions on the coefficients, whichare new even for SDEs with additive noise.

Exponential Contraction in Wasserstein Distances for Diffusion Semigroups with Negative Curvature