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- W4298097817 abstract "Motivated by classical works of Schechtman and Schmuckenschlager on intersections of $ell_p$-balls and recent ones in information-based complexity relating random sections of ellipsoids and the quality of random information in approximation problems, we study the threshold behavior of the asymptotic volume of intersections of generalized $p$-ellipsoids. The non-critical behavior is determined under a spectral flatness (Wiener entropy) condition on the semi-axes. In order to understand the critical case at the threshold, we prove a central limit theorem for $q$-norms of points sampled uniformly at random from a $p$-ellipsoid, which is obtained under Noether's condition on the semi-axes." @default.
- W4298097817 created "2022-10-01" @default.
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- W4298097817 date "2021-07-02" @default.
- W4298097817 modified "2023-09-26" @default.
- W4298097817 title "Spectral flatness and the volume of intersections of $p$-ellipsoids" @default.
- W4298097817 doi "https://doi.org/10.48550/arxiv.2107.01097" @default.
- W4298097817 hasPublicationYear "2021" @default.
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