Isoperimetric inequality for radial probability measures on Euclidean spaces |
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Authors: | Asuka Takatsu |
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Affiliation: | Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan |
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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. |
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Keywords: | Poincaré limit Isoperimetric inequality |
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