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Finite size percolation in regular trees

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  • Arias-Castro, Ery

Abstract

In the context of percolation in a regular tree, we study the size of the largest cluster and the length of the longest run starting within the first d generations. As d tends to infinity, we prove almost sure and weak convergence results.

Suggested Citation

  • Arias-Castro, Ery, 2011. "Finite size percolation in regular trees," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 302-309, February.
  • Handle: RePEc:eee:stapro:v:81:y:2011:i:2:p:302-309
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    References listed on IDEAS

    as
    1. Chen, Jihong & Huo, Xiaoming, 2006. "Distribution of the Length of the Longest Significance Run on a Bernoulli Net and Its Applications," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 321-331, March.
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