# 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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https://tel.archives-ouvertes.fr/tel-00009780
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

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• HAL Id : tel-00009780, version 1

### Citation

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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