First-passage percolation on random simple triangulations

Abstract

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(n 1/4 ) window around a constant multiple of the graph distance.(1) The author's program simtria provides a highly optimized and efficient sampler for random simple triangulations. It supports multithreading and uses efficient memory management in order to facilitate large scale simulations. The program is open source and available for free on the github: https://github.com/BenediktStufler/simtria.