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Largeur de seuil dans les lois du Zéro-Un

Abstract : This thesis further develops some recent results due to Talagrand, Friedgut and Kalai on the study of general conditions under which threshold phenomena occur. In a first part, we contribute to the unification of the general framework of the threshold phenomena, firstly by connecting the original setting of the ``threshold functions'' due to Erdös and Rényi, the one of Friedgut and Kalai's work and the concentration of the hitting time of the property for which the threshold phenomenon holds; secondly, by originating a research on the stability of threshold phenomena under three kind of operations: union, intersection and tensor product. We obtain thus a simple way to construct threshold widths of various orders. In a second part, we optimize the general upper bound on the threshold width of a monotone symmetric property by using the logarithmic Sobolev inequality on the discrete cube.
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Contributor : Raphaël Rossignol <>
Submitted on : Tuesday, July 19, 2005 - 6:04:44 PM
Last modification on : Friday, April 10, 2020 - 5:11:59 PM
Long-term archiving on: : Friday, April 2, 2010 - 10:44:36 PM


  • HAL Id : tel-00009780, version 1


Raphaël Rossignol. Largeur de seuil dans les lois du Zéro-Un. Mathématiques [math]. Université René Descartes - Paris V, 2005. Français. ⟨tel-00009780⟩



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