Abstract
We present a simple proof based on modified logarithmic Sobolev inequalities, of Talagrand's concentration inequality for the exponential distribution. We actually observe that every measure satisfying a Poincaré inequality shares the same concentration phenomenon. We also discuss exponential integrability under Poincaré inequalities and its consequence to sharp diameter upper bounds on spectral gaps.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 383-400 |
| Number of pages | 18 |
| Journal | Probability Theory and Related Fields |
| Volume | 107 |
| Issue number | 3 |
| DOIs | |
| State | Published - Mar 1997 |
| Externally published | Yes |