Uniqueness of the infinite noodle
Nicolas Curien, Gady Kozma, Vladas Sidoravicius, Laurent Tournier
TL;DR
This paper proves that a graph formed by superimposing two independent uniform infinite non-crossing perfect matchings of integers contains at most one infinite path, providing insights into the structure of such random graphs.
Contribution
It establishes the uniqueness of the infinite path in a specific random graph model formed by superimposing two independent matchings.
Findings
The graph contains at most one infinite path.
Superimposing two independent matchings results in a unique infinite path or none.
The result has implications for understanding the structure of non-crossing matchings.
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.
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