## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- Electronic Research Announcements
- Conference Publications
- AIMS Mathematics

DCDS

We provide yet another proof of the Otto-Villani theorem
from the log Sobolev inequality to the Talagrand transportation cost
inequality valid in arbitrary metric measure spaces. The argument relies on the recent
development [2] identifying gradient flows in Hilbert space and in Wassertein space,
emphasizing one key step as precisely the root of the Otto-Villani theorem.
The approach does not require the doubling property or the validity of the
local Poincaré inequality.

DCDS

We establish an improved form of the classical logarithmic Sobolev inequality for the Gaussian
measure restricted to probability densities which satisfy a Poincaré inequality.
The result implies a lower bound
on the deficit in terms of the quadratic Kantorovich-Wasserstein distance. We similarly investigate
the deficit in the Talagrand quadratic transportation cost inequality this time by means of an
${ L}^1$-Kantorovich-Wasserstein distance, optimal for product measures, and deduce a lower bound on the deficit in the logarithmic Sobolev inequality in terms of this metric. Applications are given in the context
of the Bakry-Émery theory and the coherent state transform. The proofs combine tools from
semigroup and heat kernel theory and optimal mass transportation.

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]