Poincar e ’ s inequalities and Talagrand ’ s concentration phenomenon for the exponential distribution
نویسندگان
چکیده
We present a simple proof, based on modi ed 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.
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تاریخ انتشار 1997