Accessibility percolation on n-trees

@article{Nowak2013AccessibilityPO,
  title={Accessibility percolation on n-trees},
  author={Stefan Nowak and Joachim H A Krug},
  journal={arXiv: Statistical Mechanics},
  year={2013}
}
  • S. Nowak, J. Krug
  • Published 6 February 2013
  • Mathematics
  • arXiv: Statistical Mechanics
Accessibility percolation is a new type of percolation problem inspired by evolutionary biology. To each vertex of a graph a random number is assigned and a path through the graph is called accessible if all numbers along the path are in ascending order. For the case when the random variables are independent and identically distributed, we derive an asymptotically exact expression for the probability that there is at least one accessible path from the root to the leaves in an $n$-tree. This… 
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