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?

In what sense are uniform measures on random triangulations of the sphere understood? Do you have good references?
– Igor RivinFeb 3 '11 at 15:19

@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/…
– j.c.Feb 3 '11 at 20:55

@jc: thanks! Will check it out...
– Igor RivinFeb 3 '11 at 21:51