Random metric spaces and universality

被引：32

作者：

Vershik, AA ^{[1
]}

机构：

[1] VA Steklov Math Inst, St Petersburg Branch, St Petersburg 191011, Russia

来源：

RUSSIAN MATHEMATICAL SURVEYS | 2004年 / 59卷 / 02期

关键词：

D O I：

10.1070/RM2004v059n02ABEH000718

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The notion of random metric space is defined, and it is proved that such a space is isometric to the Urysohn universal metric space with probability one. The main technique is the study of universal and random distance matrices, properties of metric (in particular, universal) spaces are related to properties of distance matrices. Examples of other categories in which randomness and universality coincide (graphs, and so on) are given.

引用

页码：259 / 295

页数：37

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