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

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

2008-10-20

arxiv.org/abs/0810.3670v3

Mathematics

Probability

minor revision

Scientific paper

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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