Isoperimetry between exponential and Gaussian

Authors:
  • FBFranck Barthe
    Franck Barthe
  • PCPatrick Cattiaux
    Patrick Cattiaux
  • CRCyril Roberto
    Cyril Roberto
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Abstract
We study in details the isoperimetric profile of product probability measures with tails between the exponential and the Gaussian regime. In particular we exhibit many examples where coordinate half-spaces are approximate solutions of the isoperimetric problem.