Geometry of spaces between polytopes and related zonotopes

Yehoram Gordon; Alexander Litvak; Carsten Schütt; Elisabeth Werner

doi:10.1016/S0007-4497(02)01139-9

Geometry of spaces between polytopes and related zonotopes

Yehoram Gordon
, Alexander Litvak
, Carsten Schütt
, Elisabeth Werner

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

17 Scopus citations

Abstract

We study geometric parameters associated with the Banach spaces ((double-struck R)ⁿ, ∥ · ∥_k,q) normed by ∥x∥_k,q = (∑_1<≤_i≤k [x, a_i] *^q)1/q, where {ai}i≤N is a given sequence of N points in (double-struck R)ⁿ, 1 ≤ k ≤ N, 1 ≤ q ≤ ∞, and {λ_i*}i≥1 denotes the decreasing rearrangement of a sequence {λ_i}_i≥1 ⊂(double-struck R).

Original language	English (US)
Pages (from-to)	733-762
Number of pages	30
Journal	Bulletin des Sciences Mathematiques
Volume	126
Issue number	9
DOIs	https://doi.org/10.1016/S0007-4497(02)01139-9
State	Published - Nov 2002
Externally published	Yes

Bibliographical note

Funding Information:
* Corresponding author. E-mail address: [email protected] (Y. Gordon). 1 Partially supported by Nato Collaborative Linkage Grant PST.CLG.977406. 2 Partially supported by France–Israel Arc-en-Ciel exchange. 3 Partially supported by the Fund for the Promotion of Research at the Technion. 4 Partially supported by a Lady Davis Fellowship. 5Partially supported by National Science Foundation Grant DMS-0072241 and by Nato Collaborative Linkage Grant PST.CLG.976356.

Keywords

Dvoretzky's theorem
Polytopes
Random variables
Volume ratio
Zonoids
p-summing norm

Publisher link

10.1016/S0007-4497(02)01139-9

Find It

Find It at U of M Libraries

Cite this

@article{3f1ceb7ba62d4e3490641a17d78c94d5,

title = "Geometry of spaces between polytopes and related zonotopes",

abstract = "We study geometric parameters associated with the Banach spaces ((double-struck R)n, ∥ · ∥k,q) normed by ∥x∥k,q = (∑1<≤i≤k [x, ai] *q)1/q, where \{ai\}i≤N is a given sequence of N points in (double-struck R)n, 1 ≤ k ≤ N, 1 ≤ q ≤ ∞, and \{λi*\}i≥1 denotes the decreasing rearrangement of a sequence \{λi\}i≥1 ⊂(double-struck R).",

keywords = "Dvoretzky's theorem, Polytopes, Random variables, Volume ratio, Zonoids, p-summing norm",

author = "Yehoram Gordon and Alexander Litvak and Carsten Sch{\"u}tt and Elisabeth Werner",

note = "Funding Information: * Corresponding author. E-mail address: [email protected] (Y. Gordon). 1 Partially supported by Nato Collaborative Linkage Grant PST.CLG.977406. 2 Partially supported by France–Israel Arc-en-Ciel exchange. 3 Partially supported by the Fund for the Promotion of Research at the Technion. 4 Partially supported by a Lady Davis Fellowship. 5Partially supported by National Science Foundation Grant DMS-0072241 and by Nato Collaborative Linkage Grant PST.CLG.976356.",

year = "2002",

month = nov,

doi = "10.1016/S0007-4497(02)01139-9",

language = "English (US)",

volume = "126",

pages = "733--762",

journal = "Bulletin des Sciences Mathematiques",

issn = "0007-4497",

publisher = "Elsevier Masson s.r.l.",

number = "9",

}

TY - JOUR

T1 - Geometry of spaces between polytopes and related zonotopes

AU - Gordon, Yehoram

AU - Litvak, Alexander

AU - Schütt, Carsten

AU - Werner, Elisabeth

N1 - Funding Information: * Corresponding author. E-mail address: [email protected] (Y. Gordon). 1 Partially supported by Nato Collaborative Linkage Grant PST.CLG.977406. 2 Partially supported by France–Israel Arc-en-Ciel exchange. 3 Partially supported by the Fund for the Promotion of Research at the Technion. 4 Partially supported by a Lady Davis Fellowship. 5Partially supported by National Science Foundation Grant DMS-0072241 and by Nato Collaborative Linkage Grant PST.CLG.976356.

PY - 2002/11

Y1 - 2002/11

N2 - We study geometric parameters associated with the Banach spaces ((double-struck R)n, ∥ · ∥k,q) normed by ∥x∥k,q = (∑1<≤i≤k [x, ai] *q)1/q, where {ai}i≤N is a given sequence of N points in (double-struck R)n, 1 ≤ k ≤ N, 1 ≤ q ≤ ∞, and {λi*}i≥1 denotes the decreasing rearrangement of a sequence {λi}i≥1 ⊂(double-struck R).

AB - We study geometric parameters associated with the Banach spaces ((double-struck R)n, ∥ · ∥k,q) normed by ∥x∥k,q = (∑1<≤i≤k [x, ai] *q)1/q, where {ai}i≤N is a given sequence of N points in (double-struck R)n, 1 ≤ k ≤ N, 1 ≤ q ≤ ∞, and {λi*}i≥1 denotes the decreasing rearrangement of a sequence {λi}i≥1 ⊂(double-struck R).

KW - Dvoretzky's theorem

KW - Polytopes

KW - Random variables

KW - Volume ratio

KW - Zonoids

KW - p-summing norm

UR - https://www.scopus.com/pages/publications/0036851208

UR - https://www.scopus.com/pages/publications/0036851208#tab=citedBy

U2 - 10.1016/S0007-4497(02)01139-9

DO - 10.1016/S0007-4497(02)01139-9

M3 - Article

AN - SCOPUS:0036851208

SN - 0007-4497

VL - 126

SP - 733

EP - 762

JO - Bulletin des Sciences Mathematiques

JF - Bulletin des Sciences Mathematiques

IS - 9

ER -

Geometry of spaces between polytopes and related zonotopes

Abstract

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this