Scaling Limits for Width Two Partially Ordered Sets: The Incomparability Window
Probability
2013-06-24 v3 Combinatorics
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.
Cite
@article{arxiv.0810.3670,
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= {arXiv preprint arXiv:0810.3670},
year = {2013}
}
Comments
minor revision