The Local Limit of Random Sorting Networks

A sorting network is a geodesic path from 12 ... n to n ... 21 in the Cayley graph of S-n generated by adjacent transpositions. For a uniformly random sorting network, we establish the existence of a local limit of the process of space-time locations of transpositions in a neighbourhood of an for a is an element of [0, 1] as n -> infinity...More