Embedded trees and the support of the ISE
Copyright policy )Embedded trees and the support of the ISE
Embedded trees are labelled rooted trees, where the root has zero label and where the labels of adjacent vertices differ (at most) by [Formula: see text]. Recently it has been proved (see Chassaing and Schaeffer (2004) [8] and Janson and Marckert (2005) [11]) that the distribution of the maximum and minimum labels are closely related to the support of the density of the integrated superbrownian excursion (ISE). The purpose of this paper is to make this probabilistic limiting relation more explicit by using a generating function approach due to Bouttier et al. (2003) [6] that is based on properties of Jacobi's [Formula: see text]-functions. In particular, we derive an integral representation of the joint distribution function of the supremum and infimum of the support of the ISE in terms of the Weierstrass [Formula: see text]-function. Furthermore we re-derive the limiting radius distribution in random quadrangulations (by Chassaing and Schaeffer (2004) [8]) with the help of exact counting generating functions.
- TU Wien Austria
integrated superbrownian excursion, Random graphs (graph-theoretic aspects), Exact enumeration problems, generating functions, integral representaion, random quadrangulations, Article, Trees, Theoretical Computer Science, Graph labelling (graceful graphs, bandwidth, etc.), Branching processes (Galton-Watson, birth-and-death, etc.), ISE, distribution function, Weierstrass \(\wp\) function, exact counting generating functions, limiting radius distribution, distribution of minimum labels, Superprocesses, labeled rooted trees, probabilistic limiting relationgenerating function approach, distribution of maximum labels, Computational Theory and Mathematics, embedded trees, Probability distributions: general theory, Jacobi theta function, Geometry and Topology
integrated superbrownian excursion, Random graphs (graph-theoretic aspects), Exact enumeration problems, generating functions, integral representaion, random quadrangulations, Article, Trees, Theoretical Computer Science, Graph labelling (graceful graphs, bandwidth, etc.), Branching processes (Galton-Watson, birth-and-death, etc.), ISE, distribution function, Weierstrass \(\wp\) function, exact counting generating functions, limiting radius distribution, distribution of minimum labels, Superprocesses, labeled rooted trees, probabilistic limiting relationgenerating function approach, distribution of maximum labels, Computational Theory and Mathematics, embedded trees, Probability distributions: general theory, Jacobi theta function, Geometry and Topology
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).3 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!