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Scaling Limits for Width Two Partially Ordered Sets: The Incomparability Window

We study the structure of a uniformly randomly chosen partial order of width 2 on n elements. We show that under the appropriate scaling, the number of incomparable elements converges to the height of a one dimensional Brownian excursion at a uniformly chosen random time in the interval [0,1], which follows the Rayleigh distribution.

preprint2010arXivOpen access
Nayantara BhatnagarNick CrawfordElchanan MosselArnab Sen
math.COmath.PR
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Open access4 authors2 topics
Imported metadata coverageMissing code, dataset, citation and institution fields are tracked without dominating the paper.Details
Citations: 0Reviews: 0Saves: 0Code: not linkedDataset: not linkedInstitutions: 0

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Nayantara BhatnagarNick CrawfordElchanan MosselArnab Sen

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