Four Talagrand inequalities under the same umbrella
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,...
Saved in:
| Main Author: | |
|---|---|
| Format: | Journal Article |
| Language: | English |
| Published: |
01-09-2019
|
| Subjects: | |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| DOI: | 10.48550/arxiv.1909.00363 |