This article is cited in 9 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.

UDC: 517.98+514

MSC: Primary 52A20, 46B20, 52A21; Secondary 46B09, 46B07

Received: 27.10.2003

DOI: 10.4213/rm706

 English version: Russian Mathematical Surveys, 2004, 59:1, 159–169

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