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arXiv · 1909.00363

Four Talagrand inequalities under the same umbrella

Michel Ledoux
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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 $\mathrm {L}^1$-$\mathrm {L}^2$ variance inequality, the quadratic transportation cost inequality, and the inequality on the supremum of empirical processes.

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Michel Ledoux. 2019-09-01. Four Talagrand inequalities under the same umbrella. https://arxiv.org/abs/1909.00363

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