From Super Poincaré to Weighted Log-Sobolev and Entropy-Cost Inequalities
| dc.creator | Wang, Feng-Yu | |
| dc.date | 2007-12-19 | |
| dc.date.accessioned | 2026-07-07T08:50:19Z | |
| dc.date.available | 2026-07-07T08:50:19Z | |
| dc.description | We derive weighted log-Sobolev inequalities from a class of super Poincaré inequalities. As an application, the Talagrand inequality with larger distances are obtained. In particular, on a complete connected Riemannian manifold, we prove that the $\log^\dd$-Sobolev inequality with $\dd\in (1,2)$ implies the $L^{2/(2-\dd)}$-transportation cost inequality $$W^\rr_{2/(2-\dd)}(fμ,μ)^{2/(2-\dd)}\le Cμ(f\log f), μ(f)=1, f\ge 0$$ for some constant $C>0$, and they are equivalent if the curvature of the corresponding generator is bounded below. Weighted log-Sobolev and entropy-cost inequalities are also derived for a large class of probability measures on $\R^d$. | |
| dc.identifier | https://arxiv.org/abs/0712.3142 | |
| dc.identifier | http://arxiv.org/abs/0712.3142 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144566 | |
| dc.subject | Probability | |
| dc.subject | Differential Geometry | |
| dc.subject | 60J60; 58G32 | |
| dc.title | From Super Poincaré to Weighted Log-Sobolev and Entropy-Cost Inequalities | |
| dc.type | text |