Geodesic
Random metric spaces and universality
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 59 (2004) no. 2, pp. 259-295

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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. 
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     title = {Random metric spaces and universality},
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A. M. Vershik. Random metric spaces and universality. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 59 (2004) no. 2, pp. 259-295. http://geodesic.mathdoc.fr/item/RM_2004_59_2_a4/