The Local Limit of Random Sorting Networks

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, pp. 412-440, 2018.

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Abstract:

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

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