Rényi divergence and \(L_p\)-affine surface area for convex bodies (Q436223)
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scientific article; zbMATH DE number 6059020
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Rényi divergence and \(L_p\)-affine surface area for convex bodies |
scientific article; zbMATH DE number 6059020 |
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Rényi divergence and \(L_p\)-affine surface area for convex bodies (English)
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20 July 2012
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The author shows that the \(L_{p}\)-affine surface areas and mixed \(p\)-affine surface areas are exponentials of Rényi divergences. Furthermore, she gives geometric interpretations for Rényi divergences \(D_{\alpha }\) of the cone measures of convex bodies for all \(\alpha\), including new ones for the relative entropy not requiring the strong smoothness and symmetry assumptions on the body.
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Rényi divergence
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relative entropy
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\(L_{p}\)-affine surface area
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