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

• Published 2013 in Order

#### Abstract

We study the structure of a uniformly randomly chosen partial order of width 2 on n elements. We analyze the local structure by studying the number of elements incomparable to a random element in the poset. 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.

DOI: 10.1007/s11083-011-9244-y

### Cite this paper

@article{Bhatnagar2013ScalingLF, title={Scaling Limits for Width Two Partially Ordered Sets: The Incomparability Window}, author={Nayantara Bhatnagar and Nick Crawford and Elchanan Mossel and Arnab Sen}, journal={Order}, year={2013}, volume={30}, pages={289-311} }