Unlacing hypercube percolation : a survey

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Abstract

The purpose of this note is twofold. First, we survey the study of the percolation phase transition on the Hamming hypercube {0,1}^m obtained in the series of papers [1,2,3,4]. Secondly, we explain how this study can be performed without the use of the so-called "lace-expansion" technique. To that aim, we provide a novel simple proof that the triangle condition holds at the critical probability. Keywords: Percolation; Phase transition; Hypercube
Original languageEnglish
Place of PublicationEindhoven
PublisherEurandom
Number of pages26
Publication statusPublished - 2013

Publication series

NameReport Eurandom
Volume2013026
ISSN (Print)1389-2355

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