Almost Euclidean sections of the N-dimensional cross-polytope using O(N) random bits

被引：5

作者：

Lovett, Shachar ^{[1
]}

Sodin, Sasha ^{[2
]}

机构：

[1] Weizmann Inst Sci, Fac Math & Comp Sci, IL-76100 Rehovot, Israel

[2] Tel Aviv Univ, Sch Math, Raymond & Beverly Sackler Fac Exact Sci, IL-69978 Tel Aviv, Israel

来源：

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2008年 / 10卷 / 04期

关键词：

almost Euclidean sections; embedding; cross-polytope; derandomization; k-wise independence;

D O I：

10.1142/S0219199708002879

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is well known that RN has subspaces of dimension proportional to N on which the l(1) norm is equivalent to the l(2) norm; however, no explicit constructions are known. Extending an earlier work by Artstein-Avidan and Milman, we prove that such a subspace can be generated using O(N) random bits.

引用

页码：477 / 489

页数：13

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