Isoperimetry and stability of hyperplanes for product probability measures

Franck Barthe (1) , Chiara Bianchini (2, 3) , Andrea Colesanti (4)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 CORIDA - Robust control of infinite dimensional systems and applications
3 IECL - Institut Élie Cartan de Lorraine
4 Dipartimento di Matematica "Ulisse Dini"

We investigate stationarity and stability of half-spaces as isoperimetric sets for product probability measures, considering the cases of coordinate and non-coordinate half-spaces. Moreover, we present several examples to which our results can be applied, with a particular emphasis on the logistic measure.

Mots clés: product measures; Poincare type inequalities; Isoperimetry; stability

Domaines: Analyse fonctionnelle [math.FA]; Probabilités [math.PR]

Franck Barthe, Chiara Bianchini, Andrea Colesanti. Isoperimetry and stability of hyperplanes for product probability measures. Annali di Matematica Pura ed Applicata, 2013, 192 (2), pp.165-190. ⟨10.1007/s10231-011-0217-y⟩. ⟨hal-00566568⟩