“…Consequences in terms of geometry, mixing, and concentration of measure have been massively investigated, and quantified by a variety of functional inequalities. The literature is too vast for an exhaustive account, and we refer the reader to the seminal papers [42,43,34,30], the survey [44], and the more recent works [24,41,21,32,40] for details, variations, references, and open problems. In particular, the present work was motivated by the following long-standing question, due to Naor and Milman, and publicized by Ollivier [44,Problem T].…”