Modified logarithmic Sobolev inequalities on R
classification
🧮 math.PR
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conditioninequalitieslogarithmicmodifiedsobolevassumptionsbobkovcompletes
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We provide a sufficient condition for a measure on the real line to satisfy a modified logarithmic Sobolev inequality, thus extending the criterion of Bobkov and G\"{o}tze. Under mild assumptions the condition is also necessary. Concentration inequalities are derived. This completes the picture given in recent contributions by Gentil, Guillin and Miclo.
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