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) |
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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 |