Abstract
We generalize the Poincaré limit which asserts that the n-dimensional Gaussian measure is approximated by the projections of the uniform probability measure on the Euclidean sphere of appropriate radius to the first n-coordinates as the dimension diverges to infinity. The generalization is done by replacing the projections with certain maps. Using this generalization, we derive a Gaussian isoperimetric inequality for an absolutely continuous probability measure on Euclidean spaces with respect to the Lebesgue measure, whose density is a radial function.
Original language | English |
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Pages (from-to) | 3435-3454 |
Number of pages | 20 |
Journal | Journal of Functional Analysis |
Volume | 266 |
Issue number | 6 |
DOIs | |
Publication status | Published - 2014 Mar 15 |
Externally published | Yes |
Keywords
- Isoperimetric inequality
- Poincaré limit
ASJC Scopus subject areas
- Analysis