Poincaré's inequalities and Talagrand's concentration phenomenon for the exponential distribution

S. Bobkov, M. Ledoux

Research output: Contribution to journalArticlepeer-review

100 Scopus citations

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 languageEnglish (US)
Pages (from-to)383-400
Number of pages18
JournalProbability Theory and Related Fields
Volume107
Issue number3
DOIs
StatePublished - Mar 1997
Externally publishedYes

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