Isoperimetry between exponential and Gaussian

Franck Barthe (1) , Patrick Cattiaux (2, 3) , Cyril Roberto (4)

1 LSP - Laboratoire de Statistique et Probabilités
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 MODAL'X - Modélisation aléatoire de Paris X
4 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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.

Domaines: Probabilités [math.PR]

Franck Barthe, Patrick Cattiaux, Cyril Roberto. Isoperimetry between exponential and Gaussian. 2007. ⟨hal-00017377v2⟩