Scaling Limits for Width Two Partially Ordered Sets: The Incomparability Window
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Statistics Papers
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width-2 partial order
scaling limits
random posets
Brownian excursion
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Statistics and Probability
scaling limits
random posets
Brownian excursion
Probability
Statistics and Probability
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Bhatnagar, Nayantara
Crawford, Nick
Mossel, Elchanan
Sen, Arnab
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Abstract
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.
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2013-03-01
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