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1 results

  • Accessibility percolation on random rooted labeled trees

  • Part of
  • Zhishui Hu, Zheng Li, Qunqiang Feng
  • Journal:
    Journal of Applied Probability / Volume 56 / Issue 2 / June 2019
    Published online by Cambridge University Press:
    30 July 2019, pp. 533-545
    Print publication:
    June 2019

  • The accessibility percolation model is investigated on random rooted labeled trees. More precisely, the number of accessible leaves (i.e. increasing paths) Zn and the number of accessible vertices Cn in a random rooted labeled tree of size n are jointly considered in this work. As n → ∞, we prove that (Zn, Cn) converges in distribution to a random vector whose probability generating function is given in an explicit form. In particular, we obtain that the asymptotic distributions of Zn + 1 and Cn are geometric distributions with parameters e/(1 + e) and 1/e, respectively. Much of our analysis is performed in the context of local weak convergence of random rooted labeled trees.