Four Talagrand inequalities under the same umbrella
arXiv:1909.00363
Abstract
This note reviews the studies of the last decades emphasizing a common principle based on entropy, logarithmic Sobolev inequality and hypercontractivity, behind four most celebrated inequalities by M. Talagrand: the convex distance inequality, the - variance inequality, the quadratic transportation cost inequality, and the inequality on the supremum of empirical processes.