@article {GENTIL2019,
	title = {An entropic interpolation proof of the HWI inequality},
	journal = {Stochastic Processes and their Applications},
	year = {2019},
	abstract = {<p>The HWI inequality is an {\textquotedblleft}interpolation{\textquotedblright}inequality between the Entropy H, the Fisher information I and the Wasserstein distance W. We present a pathwise proof of the HWI inequality which is obtained through a zero noise limit of the Schr{\"o}dinger problem. Our approach consists in making rigorous the Otto{\textendash}Villani heuristics in Otto and Villani (2000) taking advantage of the entropic interpolations, which are regular both in space and time, rather than the displacement ones.</p>},
	keywords = {Entropic interpolations, Fisher information, Relative entropy, Schr{\"o}dinger problem, Wasserstein distance},
	issn = {0304-4149},
	doi = {https://doi.org/10.1016/j.spa.2019.04.002},
	url = {http://www.sciencedirect.com/science/article/pii/S0304414918303454},
	author = {Ivan Gentil and Christian L{\'e}onard and Luigia Ripani and Luca Tamanini}
}
