The randomized dvoretzky’s theorem in ln∞ and the χ-distribution

Konstantin E. Tikhomirov

doi:10.1007/978-3-319-09477-9_31

The randomized dvoretzky’s theorem in lⁿ_∞ and the χ-distribution

Konstantin E. Tikhomirov

Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Let ε ∈ (0,1/2). We prove that if for some n > 1 and k > 1, a majority of k-dimensional sections of the ball in lⁿ_∞, is (1 + ε)-spherical then necessarily k ≤ Cε In n/ In where C is a universal constant. The bound for k: is optimal up to the choice of C.

Original language	English (US)
Pages (from-to)	455-463
Number of pages	9
Journal	Lecture Notes in Mathematics
Volume	2116
DOIs	https://doi.org/10.1007/978-3-319-09477-9_31
State	Published - 2014

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1007/978-3-319-09477-9_31

Cite this

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abstract = "Let ε ∈ (0,1/2). We prove that if for some n > 1 and k > 1, a majority of k-dimensional sections of the ball in ln∞, is (1 + ε)-spherical then necessarily k ≤ Cε In n/ In where C is a universal constant. The bound for k: is optimal up to the choice of C.",

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N2 - Let ε ∈ (0,1/2). We prove that if for some n > 1 and k > 1, a majority of k-dimensional sections of the ball in ln∞, is (1 + ε)-spherical then necessarily k ≤ Cε In n/ In where C is a universal constant. The bound for k: is optimal up to the choice of C.

AB - Let ε ∈ (0,1/2). We prove that if for some n > 1 and k > 1, a majority of k-dimensional sections of the ball in ln∞, is (1 + ε)-spherical then necessarily k ≤ Cε In n/ In where C is a universal constant. The bound for k: is optimal up to the choice of C.

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UR - https://www.scopus.com/pages/publications/84921628251#tab=citedBy

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EP - 463

JO - Lecture Notes in Mathematics

JF - Lecture Notes in Mathematics

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The randomized dvoretzky’s theorem in lⁿ_∞ and the χ-distribution

Abstract

All Science Journal Classification (ASJC) codes

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