Vershik, A. M. Random metric spaces and universality. (English. Russian original) Zbl 1065.60005 Russ. Math. Surv. 59, No. 2, 259-295 (2004); translation from Usp. Mat. Nauk 59, No. 2, 65-104 (2004). The cone \(\mathcal R\) of distance matrices is defined as \[ \mathcal R :=\{(r_{ij})_{i,j=1}^\infty : r_{ii}=0,\;r_{ij}=r_{ji}\;,\; r_{ik}+r_{kj}\geq r_{ij}, \;i,j,k=1,2,\ldots\}. \] Each element in \(\mathcal R\) generates in a natural way a (semi)-distance on \(\mathbb N\). Certain Borel probability measures on \(\mathcal R\) are defined inductively by the so-called Markovian procedure. Properties of these measures are investigated and discussed. Reviewer: Werner Linde (Jena) Cited in 2 ReviewsCited in 22 Documents MSC: 60B99 Probability theory on algebraic and topological structures 54E70 Probabilistic metric spaces 54E35 Metric spaces, metrizability Keywords:random metric spaces; Urysohn space; matrix distributions PDFBibTeX XMLCite \textit{A. M. Vershik}, Russ. Math. Surv. 59, No. 2, 259--295 (2003; Zbl 1065.60005); translation from Usp. Mat. Nauk 59, No. 2, 65--104 (2004) Full Text: DOI arXiv