Unlacing hypercube percolation: A survey

Remco van der Hofstad*, Asaf Nachmias

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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 (Borgs et al. in Random Struct Algorithms 27:137-184, 2005; Borgs et al. in Ann Probab 33:1886-1944, 2005; Borgs et al. in Combinatorica 26:395-410, 2006; van der Hofstad and Nachmias in Hypercube percolation, Preprint 2012). 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.

Original languageEnglish
Pages (from-to)23-50
Number of pages28
Issue number1
StatePublished - Jan 2014
Externally publishedYes


FundersFunder number
National Science Foundation6923910
Natural Sciences and Engineering Research Council of Canada
Nederlandse Organisatie voor Wetenschappelijk Onderzoek


    • Hypercube
    • Percolation
    • Phase transition


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