For any isotropic convex body in R^n, the subgaussian body has bounded volume ratio against the centroid body, sharp mean width O(√log n), and an orthonormal basis with subgaussian constants O(√log n).
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Geometry of the subgaussian body of an isotropic convex body
For any isotropic convex body in R^n, the subgaussian body has bounded volume ratio against the centroid body, sharp mean width O(√log n), and an orthonormal basis with subgaussian constants O(√log n).