Non-Fringe Subtrees in Conditioned Galton—Watson Trees

  • Xing Shi Cai
  • Svante Janson
DOI: https://doi.org/10.37236/7708
Keywords: Non-fringe subtrees, Galton-Watson trees, Generating functions, Singular analysis, Log-normal distribution

Abstract

We study $S(\mathcal{T}_{n})$, the number of subtrees in a conditioned Galton—Watson tree of size $n$. With two very different methods, we show that $\log(S(\mathcal{T}_{n}))$ has a Central Limit Law and that the moments of $S(\mathcal{T}_{n})$ are of exponential scale.

Published
2018-09-07
Issue
Volume 25, Issue 3 (2018)
Article Number
P3.40