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
How to Cite
Cai, X. S., & Janson, S. (2018). Non-Fringe Subtrees in Conditioned Galton—Watson Trees. The Electronic Journal of Combinatorics, 25(3), #P3.40. https://doi.org/10.37236/7708
Issue
Volume 25, Issue 3 (2018)
Article Number
P3.40