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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.

Keywords

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

R2 v1 2026-06-21T11:33:04.845Z