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- W4308755502 abstract "Let $K$ be a centrally symmetric spherical and simplicial polytope, whose vertices form a $frac{1}{4n}-$net in the unit sphere in $mathbb{R}^n$. We prove a uniform lower bound on the norms of all hyperplane projections $P: X to X$, where $X$ is the $n$-dimensional normed space with the unit ball $K$. The estimate is given in terms of the determinant function of vertices and faces of $K$. In particular, if $N geq n^{4n}$ and $K = conv { pm x_1, pm x_2, ldots, pm x_N }$, where $x_1, x_2, ldots, x_N$ are independent random points distributed uniformly in the unit sphere, then every hyperplane projection $P: X to X$ satisfies an inequality $|P|_X geq 1+c_nN^{-(2n^2+4n+6)}$ (for some explicit constant $c_n$), with the probability at least $1 - frac{3}{N}.$" @default.
- W4308755502 created "2022-11-15" @default.
- W4308755502 creator A5066589324 @default.
- W4308755502 date "2020-09-27" @default.
- W4308755502 modified "2023-10-16" @default.
- W4308755502 title "A uniform lower bound on the norms of hyperplane projections of spherical polytopes" @default.
- W4308755502 doi "https://doi.org/10.48550/arxiv.2009.12929" @default.
- W4308755502 hasPublicationYear "2020" @default.
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