Uniform measure on random triangulations of the two dimensional sphere and their limits are rather well understood. Are there any results or heuristics regarding three dimensional analogues?
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1$\begingroup$ In what sense are uniform measures on random triangulations of the sphere understood? Do you have good references? $\endgroup$– Igor RivinCommented Feb 3, 2011 at 15:19
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$\begingroup$ @Igor Rivin: B Iruth might be referring to the work by Le Gall, Miermont and others on the scaling limit(s) of planar maps, see e.g. arxiv.org/abs/1101.4856 for an introductory reference. The study of these measures is certainly not complete, but there's a reasonable body of work. On this site, see also mathoverflow.net/questions/44759/… $\endgroup$– j.c.Commented Feb 3, 2011 at 20:55
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