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Arbitrary threshold widths for monotone symmetric properties

Raphaël Rossignol
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Abstract

We investigate the threshold widths of some symmetric properties which range asymptotically between 1/\sqrt{n} and 1/(log n). These properties are built using a combination of failure sets arising from 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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Raphaël Rossignol. 2006-01-06. Arbitrary threshold widths for monotone symmetric properties. https://arxiv.org/abs/math/0601116

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