DMTCS Proceedings, Discrete Random Walks, DRW'03

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DMTCS Conference vol AC (2003), pp. 265-276


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-
non-crossing tree and (ii) the spanning subtree-size of
randomly chosen nodes in a size-
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
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