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Arbitrary Threshold Widths for Monotone, Symmetric Properties

Part of: Special processes Limit theorems Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Raphaël Rossignol
Raphaël Rossignol*
Affiliation:
Université de Neuchâtel
*
∗ 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
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Abstract

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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.

Keywords

Threshold width0-1 lawparallel-series systemseries-parallel systemk-out-of-n system

MSC classification

Primary: 60F20: Zero-one laws
Secondary: 60E15: Inequalities; stochastic orderings 60K10: Applications (reliability, demand theory, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 1 , March 2007 , pp. 164 - 180
Copyright
Copyright © Applied Probability Trust 2007 

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