✦ LIBER ✦
From super Poincaré to weighted log-Sobolev and entropy-cost inequalities
✍ Scribed by Feng-Yu Wang
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 193 KB
- Volume
- 90
- Category
- Article
- ISSN
- 0021-7824
No coin nor oath required. For personal study only.
✦ Synopsis
We derive weighted log-Sobolev inequalities from a class of super Poincaré inequalities. As an application, Talagrand inequalities with super quadratic cost functions are obtained. In particular, on a complete connected Riemannian manifold, we prove that the log δ -Sobolev inequality with δ ∈ (1, 2) implies the L 2/(2-δ) -transportation cost inequality:
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 .