On a T1 transport inequality for the adapted Wasserstein distance
Abstract
The L1 transport-entropy inequality (or T1 inequality), which bounds the 1-Wasserstein distance in terms of the relative entropy, is known to characterize Gaussian concentration. To extend the T1 inequality to laws of discrete-time processes while preserving their temporal structure, we investigate the adapted T1 inequality which relates the 1-adapted Wasserstein distance to the relative entropy. Building on the Bolley–Villani inequality, we establish the adapted T1 inequality under the same moment assumption as the classical T1 inequality.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Connexins and lens biology
Statistical Mechanics and Entropy
Publication details
- Journal / source
- Electronic Communications in Probability
- Volume
- 31
- Issue
- none
- Publication date
- 1 January 2026