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Uspekhi Mat. Nauk, 2004, Volume 59, Issue 1(355), Pages 157–168 (Mi umn706)  

This article is cited in 3 scientific papers (total in 3 papers)

Phenomena arising from high dimensionality

V. D. Milman

Tel Aviv University, School of Mathematical Sciences

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 are analyzed.

DOI: https://doi.org/10.4213/rm706

Full text: PDF file (274 kB)
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English version:
Russian Mathematical Surveys, 2004, 59:1, 159–169

Bibliographic databases:

UDC: 517.98+514
MSC: Primary 52A20, 46B20, 52A21; Secondary 46B09, 46B07
Received: 27.10.2003

Citation: V. D. Milman, “Phenomena arising from high dimensionality”, Uspekhi Mat. Nauk, 59:1(355) (2004), 157–168; Russian Math. Surveys, 59:1 (2004), 159–169

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Milman V.D., “Geometrization of probability”, In Memory of Alexander Reznikov, Progress in Mathematics, 265, 2008, 647–667  crossref  mathscinet  zmath  isi
    2. Naor A., “Quantitative Geometry”, Proc. Natl. Acad. Sci. U. S. A., 110:48 (2013), 19202–19205  crossref  mathscinet  zmath  adsnasa  isi
    3. V. A. Zorich, “Multidimensional geometry, functions of many variables and probability”, Theory Probab. Appl., 59:3 (2015), 481–493  mathnet  crossref  crossref  mathscinet  isi  elib  elib
  • Успехи математических наук Russian Mathematical Surveys
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