• Mathematics, Computer Science
  • Published in Random Struct. Algorithms 2014
  • DOI:10.1002/rsa.20481

Random non-crossing plane configurations: A conditioned Galton-Watson tree approach

@article{Curien2014RandomNP,
  title={Random non-crossing plane configurations: A conditioned Galton-Watson tree approach},
  author={Nicolas Curien and Igor Kortchemski},
  journal={Random Struct. Algorithms},
  year={2014},
  volume={45},
  pages={236-260}
}
We study various models of random non-crossing configurations consisting of diagonals of convex polygons, and focus in particular on uniform dissections and non-crossing trees. For both these models, we prove convergence in distribution towards Aldous' Brownian triangulation of the disk. In the case of dissections, we also refine the study of the maximal vertex degree and validate a conjecture of Bernasconi, Panagiotou and Steger. Our main tool is the use of an underlying Galton-Watson tree… CONTINUE READING

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