https://hal.inria.fr/hal-01183922Panholzer, AloisAloisPanholzerWien - Institut für Algebra und Computermathematik - TU Wien - Vienna University of TechnologyNon-crossing trees revisited: cutting down and spanning subtreesHAL CCSD2003Non-crossing treesgenerating functionlimiting distributions[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS][INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM][MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO][INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG]Episciences Iam, CoordinationCyril Banderier and Christian Krattenthaler2015-08-12 09:06:362021-10-13 19:58:042015-08-13 09:08:04enConference papershttps://hal.inria.fr/hal-01183922/document10.46298/dmtcs.3327application/pdf1Here 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.