Stufler, B. (2024). First-passage percolation on random simple triangulations. ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, XXI, 129–178. https://doi.org/10.30757/ALEA.v21-07
We study first-passage percolation on random simple triangulations and their dual maps with independent identically distributed link weights. Our main result shows that the first-passage percolation distance concentrates in an op(n¹/⁴) window around a constant multiple of the graph distance. Our approach follows the proof strategy by Curien and Le Gall (Ann. Sci. Éc. Norm. Supér., 2019), but we have to overcome several obstacles specific to simple triangulations.
