Around the entropic Talagrand inequality

Understand

In this article we study generalization of the classical Talagrand transport-entropy inequality in which the Wasserstein distance is replaced by the entropic transportation cost.

• This class of inequalities has been introduced in the recent work [9], in connection with the study of Schr\"odinger bridges.
• We provide several equivalent characterizations in terms of reverse hypercontractivity for the heat semigroup, contractivity of the Hamilton-Jacobi-Bellman semigroup and dimension-free concentration of measure.
• Properties such as tensorization and relations to other functional inequalities are also investigated.