Phase Transition for Accessibility Percolation on Hypercubes

Li Li ()
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Li Li: University of Chicago

Journal of Theoretical Probability, 2018, vol. 31, issue 4, 2072-2111

Abstract: Abstract In this paper, we consider accessibility percolation on hypercubes, i.e., we place i.i.d. uniform [0, 1] random variables on vertices of a hypercube, and study whether there is a path connecting two vertices such that the values of these random variables increase along the path. We establish a sharp phase transition depending on the difference of the values at the two endpoints and determine the critical window of the phase transition. Our result completely resolves a conjecture of Berestycki et al. (Accessibility percolation with backsteps. Preprint, available at http://arxiv.org/abs/1401.6894 ).

Keywords: Accessibility percolation; Hypercube; Phase transition; Second moment method; 60J80; 60G18 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-017-0769-x

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