Stochastic proof of the sharp symmetrized Talagrand inequality - Courtade, Thomas A.; Fathi, Max; Mikulincer, Dan (Comptes Rendus. Mathématique)
A new proof of the sharp symmetrized form of Talagrand’s transport-entropy inequality is given. Compared to stochastic proofs of other Gaussian functional inequalities, the new idea here is a certain coupling induced by time-reversed martingale representations.