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Russian Mathematical Surveys, 2004, Volume 59, Issue 2, Pages 259–295
DOI: https://doi.org/10.1070/RM2004v059n02ABEH000718 (Mi rm718) 		 
This article is cited in 66 scientific papers (total in 67 papers)

Random metric spaces and universality

A. M. Vershik

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
English version PDF (430 kB) Citations (67) Russian version article
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DOI: https://doi.org/10.1070/RM2004v059n02ABEH000718
Abstract: 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.
Received: 09.12.2003
Bibliographic databases:
Document Type: Article
UDC: 519.212.2+515.124.4
MSC: Primary 54E35, 54C25, 54E70; Secondary 28D99, 05C80, 15A50, 54E20, 60D05, 60B05
Language: English
Original paper language: Russian
Citation: A. M. Vershik, “Random metric spaces and universality”, Russian Math. Surveys, 59:2 (2004), 259–295
Citation in format AMSBIB
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\paper Random metric spaces and universality
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\pages 259--295
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    • This publication is cited in the following 67 articles:
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