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Scaling Limits for Width Two Partially Ordered Sets: The Incomparability Window |
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| Authors: | Nayantara Bhatnagar Nick Crawford Elchanan Mossel Arnab Sen |
| Affiliation: | 1. Department of Statistics, University of California, Berkeley, CA, USA 2. Department of Statistics and Department of Computer Science, University of California, Berkeley, CA, USA 3. Statistical Laboratory, University of Cambridge, Cambridge, UK |
| 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. |
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