From discrete to continuous percolation in dimensions 3 to 7

  title={From discrete to continuous percolation in dimensions 3 to 7},
  author={Zbigniew Koza and Jakub Pola},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  • Z. KozaJ. Pola
  • Published 26 June 2016
  • Mathematics, Computer Science
  • Journal of Statistical Mechanics: Theory and Experiment
We propose a method of studying the continuous percolation of aligned objects as a limit of a corresponding discrete model. We show that the convergence of a discrete model to its continuous limit is controlled by a power-law dependency with a universal exponent θ=3/2. This allows us to estimate the continuous percolation thresholds in a model of aligned hypercubes in dimensions d=3,…,7 with accuracy far better than that attained using any other method before. We also report improved values of… 

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