Almost Euclidean sections in symmetric spaces and concentration of order statistics

Konstantin E. Tikhomirov

doi:10.1016/j.jfa.2013.06.008

Almost Euclidean sections in symmetric spaces and concentration of order statistics

Konstantin E. Tikhomirov

Mathematics

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

5 Scopus citations

Abstract

We prove that for any symmetric n-dimensional normed space E and any ε. >. 0, E contains a (1. +. ε)-Euclidean subspace of dimension at least cln. n/ln(1/ε), where c is an absolute constant. The proof is based on a concentration property of order statistics of random vectors with i.i.d. coordinates.

Original language	English (US)
Pages (from-to)	2074-2088
Number of pages	15
Journal	Journal of Functional Analysis
Volume	265
Issue number	9
DOIs	https://doi.org/10.1016/j.jfa.2013.06.008
State	Published - Nov 1 2013

All Science Journal Classification (ASJC) codes

Analysis

Keywords

Dvoretzky's theorem
Order statistic
Symmetric basis

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10.1016/j.jfa.2013.06.008

Cite this

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title = "Almost Euclidean sections in symmetric spaces and concentration of order statistics",

abstract = "We prove that for any symmetric n-dimensional normed space E and any ε. >. 0, E contains a (1. +. ε)-Euclidean subspace of dimension at least cln. n/ln(1/ε), where c is an absolute constant. The proof is based on a concentration property of order statistics of random vectors with i.i.d. coordinates.",

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T1 - Almost Euclidean sections in symmetric spaces and concentration of order statistics

AU - Tikhomirov, Konstantin E.

PY - 2013/11/1

Y1 - 2013/11/1

N2 - We prove that for any symmetric n-dimensional normed space E and any ε. >. 0, E contains a (1. +. ε)-Euclidean subspace of dimension at least cln. n/ln(1/ε), where c is an absolute constant. The proof is based on a concentration property of order statistics of random vectors with i.i.d. coordinates.

AB - We prove that for any symmetric n-dimensional normed space E and any ε. >. 0, E contains a (1. +. ε)-Euclidean subspace of dimension at least cln. n/ln(1/ε), where c is an absolute constant. The proof is based on a concentration property of order statistics of random vectors with i.i.d. coordinates.

KW - Dvoretzky's theorem

KW - Order statistic

KW - Symmetric basis

UR - https://www.scopus.com/pages/publications/84881377902

UR - https://www.scopus.com/pages/publications/84881377902#tab=citedBy

U2 - 10.1016/j.jfa.2013.06.008

DO - 10.1016/j.jfa.2013.06.008

M3 - Article

AN - SCOPUS:84881377902

SN - 0022-1236

VL - 265

SP - 2074

EP - 2088

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 9

ER -

Almost Euclidean sections in symmetric spaces and concentration of order statistics

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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