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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.
The final publication is available at Springer via http://dx.doi.org/10.1007/s11083-011-9244-y.
width-2 partial order, scaling limits, random posets, Brownian excursion
Bhatnagar, N., Crawford, N., Mossel, E., & Sen, A. (2013). Scaling Limits for Width Two Partially Ordered Sets: The Incomparability Window. Order, 30 (1), 289-311. http://dx.doi.org/10.1007/s11083-011-9244-y
Date Posted: 27 November 2017
This document has been peer reviewed.