Uniqueness of the infinite noodle
Nicolas Curien, Gady Kozma, Vladas Sidoravičius, Laurent Tournier · Annales de l’Institut Henri Poincaré D Combinatorics Physics and their Interactions · 2019
Consider the graph obtained by superposition of an independent pair of uniform infinite non-crossing perfect matchings of the set of integers. We prove that this graph contains at most one infinite path. Several motivations are discussed.