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Abstract: . We generalize the notion of a "threshold function" from random graph theory: given a poset with an upwards closed subposet, we ask when a random process going up the poset reaches the subposet. We present a measure-theoretic generalization of a splitting argument to prove that in many such processes, all `upwards closed' properties have `weak thresholds'. Contents 0. Introductory : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 1. Processionals : : : : : : : : : ... (Update)
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0.5: Phase Transitions in the Evolution of Partial Orders - Prömel, Steger, Taraz (2000) (Correct)
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BibTeX entry: (Update)
@misc{ mccolm-weak,
author = "Gregory L. McColm",
title = "Weak Thresholds",
url = "citeseer.ist.psu.edu/mccolm96weak.html" }
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3 A Splitting Inequality (context) - McColm
2 Asymptotic Properties of Random Interval Graphs and their Us.. (context) - Godehardt, Harris
2 First Order Zero-One Laws for Random Graphs on the Circle (context) - McColm
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Documents on the same site (http://www.math.usf.edu/~mccolm/Research.html): More
MSO Zero One Laws on Random Acyclic Graphs - McColm (1999) (Correct)
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