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Four Talagrand inequalities under the same umbrella

Probability 2019-09-04 v1

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 L1\mathrm {L}^1-L2\mathrm {L}^2 variance inequality, the quadratic transportation cost inequality, and the inequality on the supremum of empirical processes.

Keywords

Cite

@article{arxiv.1909.00363,
  title  = {Four Talagrand inequalities under the same umbrella},
  author = {Michel Ledoux},
  journal= {arXiv preprint arXiv:1909.00363},
  year   = {2019}
}
R2 v1 2026-06-23T11:02:28.980Z