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

S. Bobkov; M. Ledoux

doi:10.1007/s004400050090

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

S. Bobkov, M. Ledoux

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	383-400
Number of pages	18
Journal	Probability Theory and Related Fields
Volume	107
Issue number	3
DOIs	https://doi.org/10.1007/s004400050090
State	Published - Mar 1997
Externally published	Yes

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title = "Poincar{\'e}'s inequalities and Talagrand's concentration phenomenon for the exponential distribution",

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 Poincar{\'e} inequality shares the same concentration phenomenon. We also discuss exponential integrability under Poincar{\'e} inequalities and its consequence to sharp diameter upper bounds on spectral gaps.",

author = "S. Bobkov and M. Ledoux",

year = "1997",

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volume = "107",

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AU - Ledoux, M.

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AB - 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.

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JF - Probability Theory and Related Fields

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