Lévy–Gromov’s isoperimetric inequality for an infinite dimensional diffusion generator |
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Authors: | D Bakry M Ledoux |
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Institution: | (1) Département de Mathématiques, Laboratoire de Statistique et Probabilités associé au CNRS, Université Paul–Sabatier, F-31062 Toulouse, France, FR |
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Abstract: | We establish, by simple semigroup arguments, a Lévy–Gromov isoperimetric inequality for the invariant measure of an infinite
dimensional diffusion generator of positive curvature with isoperimetric model the Gaussian measure. This produces in particular
a new proof of the Gaussian isoperimetric inequality. This isoperimetric inequality strengthens the classical logarithmic
Sobolev inequality in this context. A local version for the heat kernel measures is also proved, which may then be extended
into an isoperimetric inequality for the Wiener measure on the paths of a Riemannian manifold with bounded Ricci curvature.
Oblatum 19-VI-1995 |
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Keywords: | |
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