The Archimedean limit of random sorting networks

Abstract: Consider a list of n particles labelled in increasing order. A sorting network is a way of sorting this list into decreasing order by swapping adjacent particles, using as few swaps as possible. Simulations of large-n uniform random sorting networks reveal a surprising and beautiful global structure involving sinusoidal particle trajectories, a semicircle law, and a theorem of Archimedes. Based on these simulations, Angel, Holroyd, Romik, and Virag made a series of conjectures about the limiting behaviour of sorting networks. In this talk, I will discuss how to use the local structure and combinatorics of random sorting networks to prove these conjectures.

computational geometrydiscrete mathematicsdata structures and algorithmscombinatorics

Audience: researchers in the discipline

Discrete and Computational Geometry Seminar in Paris

Series comments: Language is English if anyone in the audience prefers it (otherwise French).

Links and passwords for the talks are on the seminar homepage: monge.univ-mlv.fr/~hubard/GAC/