Unlacing hypercube percolation: a survey

Remco Hofstad () and Asaf Nachmias ()

Metrika: International Journal for Theoretical and Applied Statistics, 2014, vol. 77, issue 1, 23-50

Abstract: The purpose of this note is twofold. First, we survey the study of the percolation phase transition on the Hamming hypercube $$\{0,1\}^{m}$$ { 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. Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: Percolation; Phase transition; Hypercube (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:metrik:v:77:y:2014:i:1:p:23-50

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DOI: 10.1007/s00184-013-0473-5

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