Discrete Random Walks, DRW'03
Cyril Banderier and Christian Krattenthaler (eds.)
DMTCS Conference Volume AC (2003), pp. 265-276
| author: | Alois Panholzer |
|---|---|
| title: | Non-crossing trees revisited: cutting down and spanning subtrees |
| keywords: | Non-crossing trees, generating function, limiting distributions |
| abstract: |
Here we consider two parameters for random non-crossing
trees: (i) the number of random cuts to destroy a
size-
n
non-crossing tree and (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 (ii) as a functional of a conditioned
random walk, and although we do not have such an
interpretation for parameter (i), we obtain here
limiting distributions, that are also arising as limits of
some functionals of conditioned random walks.
|
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| reference: | Alois Panholzer (2003), Non-crossing trees revisited: cutting down and spanning subtrees, in Discrete Random Walks, DRW'03, Cyril Banderier and Christian Krattenthaler (eds.), Discrete Mathematics and Theoretical Computer Science Proceedings AC, pp. 265-276 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
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