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

##### Authors
Bhatnagar, Nayantara
Crawford, Nick
Mossel, Elchanan
Sen, Arnab
##### Description
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.
Comment: minor revision
##### Keywords
Mathematics - Probability, Mathematics - Combinatorics, 60C05