Quadratic Transportation Cost and Talagrand’s Inequality
In this chapter, we prove Talagrand’s convex distance inequality via the transportation cost method, an approach pioneered by Kati Marton  and further developed by Amir Dembo . This approach is particularly interesting because:
• It places both the theorem and its proof in its natural place within the context of isoperimetric inequalities.
• It places a standard structure on the proof as opposed to the somewhat ad hoc nature of the original inductive proof of Talagrand.
• It isolates very clearly the essential content of the proof in one dimension and shows that the extension to higher dimensions is routine.
• It also allows a stronger version of the method ...