Coupling via Pathwise Time Reversal

Many functional inequalities admit short and elegant proofs when approached through stochastic analysis. Often, the key step is to identify a natural coupling between Brownian motions, which in the simplest cases can be done in a trivial way. In this talk, we will describe a setting where the trivial approach fails, and where a more subtle coupling, obtained through time reversal of the Wiener space, plays a crucial role. In certain cases, this coupling even turns out to be optimal.