Uniqueness of the infinite noodle

Nicolas Curien; Gady Kozma; Vladas Sidoravicius; Laurent Tournier

doi:10.4171/AIHPD/70

Uniqueness of the infinite noodle

Nicolas Curien, Gady Kozma, Vladas Sidoravicius, Laurent Tournier

Department of Mathematics

Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	221-238
Number of pages	18
Journal	Annales de l'Institut Henri Poincare (D) Combinatorics, Physics and their Interactions
Volume	6
Issue number	2
Early online date	20 Mar 2019
DOIs	https://doi.org/10.4171/AIHPD/70
State	Published - 2019

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Algebra and Number Theory
Statistics and Probability
Geometry and Topology
Discrete Mathematics and Combinatorics

Access to Document

10.4171/AIHPD/70

http://arxiv.org/abs/1701.01083License: Other

Cite this

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title = "Uniqueness of the infinite noodle",

abstract = "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.",

author = "Nicolas Curien and Gady Kozma and Vladas Sidoravicius and Laurent Tournier",

note = "1 The research of N. Curien and L. Tournier was supported by MathAmSud grant LSBS2014. 2 The research of G. Kozma was supported by the Israel Science Foundationn, by the Jesselson Foundation, and by Paul and Tina Gardner. 3 The research of V. Sidoravicius supported by NSFC grant 11771292 and by National Thousand Talent Prog Acknowledgment. We would like to thank Omer Angel for fruitful discussions in particular about parity arguments in the proof of the last section.",

year = "2019",

doi = "10.4171/AIHPD/70",

language = "الإنجليزيّة",

volume = "6",

pages = "221--238",

journal = "Annales de l'Institut Henri Poincare (D) Combinatorics, Physics and their Interactions",

issn = "2308-5827",

publisher = "European Mathematical Society Publishing House",

number = "2",

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T1 - Uniqueness of the infinite noodle

AU - Curien, Nicolas

AU - Kozma, Gady

AU - Sidoravicius, Vladas

AU - Tournier, Laurent

N1 - 1 The research of N. Curien and L. Tournier was supported by MathAmSud grant LSBS2014. 2 The research of G. Kozma was supported by the Israel Science Foundationn, by the Jesselson Foundation, and by Paul and Tina Gardner. 3 The research of V. Sidoravicius supported by NSFC grant 11771292 and by National Thousand Talent Prog Acknowledgment. We would like to thank Omer Angel for fruitful discussions in particular about parity arguments in the proof of the last section.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

U2 - 10.4171/AIHPD/70

DO - 10.4171/AIHPD/70

M3 - مقالة

SN - 2308-5827

VL - 6

SP - 221

EP - 238

JO - Annales de l'Institut Henri Poincare (D) Combinatorics, Physics and their Interactions

JF - Annales de l'Institut Henri Poincare (D) Combinatorics, Physics and their Interactions

IS - 2

ER -