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.
Bibliographical noteFunding Information:
A. Sen was supported by DOD ONR grant N0014-07-1-05-06, DMS 0528488, and DMS 0548249 (CAREER).
N. Bhatnagar was supported by DOD ONR grant N0014-07-1-05-06 and DMS 0528488.
N. Crawford was supported by DMS 0548249 (CAREER).
- Brownian excursion
- Random posets
- Scaling limits
- Width-2 partial order