Random polytopes in products of balls with block-beta sampling have expected facet counts of order n^{(k-1)/(k+1)} (ln n)^{c}, bridging smooth and polytopal cases.
Artstein-Avidan, A
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Random polytopes in convex bodies: Bridging the gap between extremal containers
Random polytopes in products of balls with block-beta sampling have expected facet counts of order n^{(k-1)/(k+1)} (ln n)^{c}, bridging smooth and polytopal cases.