Finite size percolation in regular trees

Ery Arias-Castro

Statistics & Probability Letters, 2011, vol. 81, issue 2, 302-309

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.

Keywords: Percolation; on; trees; Largest; open; cluster; Longest; success; run; Galton-Watson; processes; Chen-Stein; method; for; Poisson; approximation (search for similar items in EconPapers)
Date: 2011
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