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Annales de l’Institut Henri Poincaré D

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Volume 6, Issue 2, 2019, pp. 221–238
DOI: 10.4171/AIHPD/70

Published online: 2019-03-20

Uniqueness of the infinite noodle

Nicolas Curien[1], Gady Kozma[2], Vladas Sidoravicius[3] and Laurent Tournier[4]

(1) Université Paris-Sud, Orsay, France
(2) Weizmann Institute of Science, Rehovot, Israel
(3) Courant Institute of Mathematical Sciences, New York, USA and NYU at Shanghai, China
(4) Université Paris 13, Sorbonne Paris Cité, France

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.

Keywords: Infinite cluster, random matching

Curien Nicolas, Kozma Gady, Sidoravicius Vladas, Tournier Laurent: Uniqueness of the infinite noodle. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 6 (2019), 221-238. doi: 10.4171/AIHPD/70