Quenched Survival of Bernoulli Percolation on Galton-Watson Trees

  title={Quenched Survival of Bernoulli Percolation on Galton-Watson Trees},
  author={Marcus Michelen and R. Pemantle and J. Rosenberg},
  journal={arXiv: Probability},
  • Marcus Michelen, R. Pemantle, J. Rosenberg
  • Published 2018
  • Mathematics
  • arXiv: Probability
  • We explore the survival function for percolation on Galton-Watson trees. Letting $g(T,p)$ represent the probability a tree $T$ survives Bernoulli percolation with parameter $p$, we establish several results about the behavior of the random function $g(\mathbf{T} , \cdot)$, where $\mathbf{T}$ is drawn from the Galton-Watson distribution. These include almost sure smoothness in the supercritical region; an expression for the $k\text{th}$-order Taylor expansion of $g(\mathbf{T} , \cdot)$ at… CONTINUE READING
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