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Characterization of Gaussian measures by the isoperimetric property of half-spaces

✍ Scribed by S. G. Bobkov; C. Houdré

Publisher
Springer US
Year
1999
Tongue
English
Weight
371 KB
Volume
93
Category
Article
ISSN
1573-8795

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📜 SIMILAR VOLUMES

A Functional Form of the Isoperimetric I
A Functional Form of the Isoperimetric Inequality for the Gaussian Measure
✍ S. Bobkov 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 367 KB

Let g be a smooth function on R n with values in [0, 1]. Using the isoperimetric property of the Gaussian measure, it is proved that ,(8 &1 (Eg))&E,(8 &1 ( g)) E |{g|. Conversely, this inequality implies the isoperimetric property of the Gaussian measure.

Extremal Properties of Central Half-Spac
Extremal Properties of Central Half-Spaces for Product Measures
✍ F. Barthe 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 216 KB

We deal with the isoperimetric and the shift problem for subsets of measure 1Â2 in product probability spaces. We prove that the canonical central half-spaces are extremal in particular cases: products of log-concave measures on the real line satisfying precise conditions and products of uniform mea