Asymptotics of trees with a prescribed degree sequence and applications

  title={Asymptotics of trees with a prescribed degree sequence and applications},
  author={Nicolas Broutin and Jean-François Marckert},
  journal={Random Struct. Algorithms},
Let t be a rooted tree and ni(t) the number of nodes in t having i children. The degree sequence (ni(t), i ≥ 0) of t satisfies ∑ i≥0 ni(t) = 1 + ∑ i≥0 ini(t) = |t|, where |t| denotes the number of nodes in t. In this paper, we consider trees sampled uniformly among all plane trees having the same degree sequence s; we write Ps for the corresponding distribution. Let s(κ) = (ni(κ), i ≥ 0) be a list of degree sequences indexed by κ corresponding to trees with size nκ → +∞. We show that under some… CONTINUE READING


Publications referenced by this paper.
Showing 1-10 of 50 references

Brownian excursions

  • D. Aldous
  • critical random graphs and the multiplicative…
  • 1997
Highly Influential
8 Excerpts

The height and width of random tree with a fixed

  • L. Addario-Berry
  • “finite variance” degree sequence. arXiv:1109…
  • 2011
Highly Influential
4 Excerpts

Convergence of discrete snakes

  • S. Janson, J.-F. Marckert
  • J. Theoret. Probab., 18(3):615–647
  • 2005
Highly Influential
6 Excerpts

The depth first processes of Galton-Watson trees converge to the same Brownian excursion

  • J. Marckert, A. Mokkadem
  • Ann. Probab., 31(3):1655–1678
  • 2003
Highly Influential
6 Excerpts

Convergence of probability measures

  • P. Billingsley
  • Wiley Series in Probability and Statistics…
  • 1999
Highly Influential
3 Excerpts

Invariance principles for conditioned galton-watson trees

  • I. Kortchemski
  • Arxiv:1110.2163
  • 2011
2 Excerpts

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