Unlacing hypercube percolation: A survey

Remco van der Hofstad*, Asaf Nachmias

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 (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
JournalMetrika
Volume77
Issue number1
DOIs
StatePublished - Jan 2014
Externally publishedYes

Keywords

  • Hypercube
  • Percolation
  • Phase transition

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