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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 289-311 |
| Number of pages | 23 |
| Journal | Order |
| Volume | 30 |
| Issue number | 1 |
| DOIs | |
| State | Published - Mar 2013 |
Bibliographical note
Funding Information:A. Sen was supported by DOD ONR grant N0014-07-1-05-06, DMS 0528488, and DMS 0548249 (CAREER).
Funding Information:
N. Bhatnagar was supported by DOD ONR grant N0014-07-1-05-06 and DMS 0528488.
Funding Information:
N. Crawford was supported by DMS 0548249 (CAREER).
Keywords
- Brownian excursion
- Random posets
- Scaling limits
- Width-2 partial order
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