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Arbitrary Threshold Widths for Monotone, Symmetric Properties

  • Raphaël Rossignol (a1)

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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Copyright

Corresponding author

Postal address: Institut de Mathématiques, Faculté des Sciences, Université de Neuchâtel, 11 rue Emile Argand, case postal 158, 2009 Neuchâtel, Switzerland. Email address: raphael.rossignol@unine.ch

References

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Arbitrary Threshold Widths for Monotone, Symmetric Properties

  • Raphaël Rossignol (a1)

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