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Arbitrary Threshold Widths for Monotone, Symmetric Properties
Published online by Cambridge University Press: 14 July 2016
Abstract
We show that there exist symmetric properties in the discrete n-cube whose threshold widths range asymptotically between 1/√n and 1/logn. These properties are built using a combination of failure sets arising in reliability theory. This combination of sets is simply called a product. Some general results on the threshold width of the product of two sets A and B in terms of the threshold locations and widths of A and B are provided.
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- Research Article
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- Copyright © Applied Probability Trust 2007
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