Corpus ID: 202617703

PR ] 3 J un 2 01 8 Critical Percolation and the Incipient Infinite Cluster on Galton-Watson Trees

@inproceedings{Michelen2018PR3,
  title={PR ] 3 J un 2 01 8 Critical Percolation and the Incipient Infinite Cluster on Galton-Watson Trees},
  author={M. Michelen},
  year={2018}
}
We consider critical percolation on Galton-Watson trees and prove quenched analogues of classical theorems of critical branching processes. We show that the probability critical percolation reaches depth n is asymptotic to a tree-dependent constant times n. Similarly, conditioned on critical percolation reaching depth n, the number of vertices at depth n in the critical percolation cluster almost surely converges in distribution to an exponential random variable with mean depending only on the… Expand

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