Non-crossing trees revisited: cutting down and spanning subtrees
Abstrak
Here we consider two parameters for random non-crossing trees: $\textit{(i)}$ the number of random cuts to destroy a size-$n$ non-crossing tree and $\textit{(ii)}$ the spanning subtree-size of $p$ randomly chosen nodes in a size-$n$ non-crossing tree. For both quantities, we are able to characterise for $n → ∞$ the limiting distributions. Non-crossing trees are almost conditioned Galton-Watson trees, and it has been already shown, that the contour and other usually associated discrete excursions converge, suitable normalised, to the Brownian excursion. We can interpret parameter $\textit{(ii)}$ as a functional of a conditioned random walk, and although we do not have such an interpretation for parameter $\textit{(i)}$, we obtain here limiting distributions, that are also arising as limits of some functionals of conditioned random walks.
Topik & Kata Kunci
Penulis (1)
Alois Panholzer
Akses Cepat
- Tahun Terbit
- 2003
- Sumber Database
- DOAJ
- DOI
- 10.46298/dmtcs.3327
- Akses
- Open Access ✓