Phenomena arising from high dimensionality

V. Milman

doi:10.1070/RM2004v059n01ABEH000706

Phenomena arising from high dimensionality

V. Milman^*

^*Corresponding author for this work

School of Mathematical Sciences

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

5 Scopus citations

Abstract

Some general properties are discussed for normed spaces (or, equivalently, convex bodies) that are finite-dimensional of very high dimension. It turns out that these objects show much less diversity than one could expect a priori. Next, some asymptotic phenomena that govern (in the author's opinion) the asymptotic behaviour of systems of large dimension axe analyzed.

Original language	English
Pages (from-to)	159-169
Number of pages	11
Journal	Russian Mathematical Surveys
Volume	59
Issue number	1
DOIs	https://doi.org/10.1070/RM2004v059n01ABEH000706
State	Published - 2004

Access to Document

10.1070/RM2004v059n01ABEH000706

Cite this

@article{43b47641fb5c449cb06d1db32180b07e,

title = "Phenomena arising from high dimensionality",

abstract = "Some general properties are discussed for normed spaces (or, equivalently, convex bodies) that are finite-dimensional of very high dimension. It turns out that these objects show much less diversity than one could expect a priori. Next, some asymptotic phenomena that govern (in the author's opinion) the asymptotic behaviour of systems of large dimension axe analyzed.",

author = "V. Milman",

year = "2004",

doi = "10.1070/RM2004v059n01ABEH000706",

language = "אנגלית",

volume = "59",

pages = "159--169",

journal = "Russian Mathematical Surveys",

issn = "0036-0279",

publisher = "Steklov Mathematical Institute of Russian Academy of Sciences",

number = "1",

}

TY - JOUR

T1 - Phenomena arising from high dimensionality

AU - Milman, V.

PY - 2004

Y1 - 2004

N2 - Some general properties are discussed for normed spaces (or, equivalently, convex bodies) that are finite-dimensional of very high dimension. It turns out that these objects show much less diversity than one could expect a priori. Next, some asymptotic phenomena that govern (in the author's opinion) the asymptotic behaviour of systems of large dimension axe analyzed.

AB - Some general properties are discussed for normed spaces (or, equivalently, convex bodies) that are finite-dimensional of very high dimension. It turns out that these objects show much less diversity than one could expect a priori. Next, some asymptotic phenomena that govern (in the author's opinion) the asymptotic behaviour of systems of large dimension axe analyzed.

UR - https://www.scopus.com/pages/publications/3042731582

U2 - 10.1070/RM2004v059n01ABEH000706

DO - 10.1070/RM2004v059n01ABEH000706

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:3042731582

SN - 0036-0279

VL - 59

SP - 159

EP - 169

JO - Russian Mathematical Surveys

JF - Russian Mathematical Surveys

IS - 1

ER -

Phenomena arising from high dimensionality

Abstract

Access to Document

Other files and links

Fingerprint

Cite this