Some bounds on probabilistic distances via integration by parts formulae

Appears in collection : 2022 - T3 - WS3 - Measure-theoretic Approaches and Optimal Transportation in Statistics

I will review a recent stream of research, dealing with the control of Wasserstein-type (and more general) probabilistic distances, both in uni- and multi-variate settings, by using infinite-dimensional integration by parts formulae. I will illustrate my presentation with examples from stochastic geometry (random geometric graphs and the geometry of Gaussian fields), and evoke several connections with generalized logarithmic Sobolev and concentration estimates.