A Central Limit Theorem for the Number of Degree-k Vertices in Random Maps

A Central Limit Theorem for the Number of Degree-k Vertices in Random Maps

We prove that the number of vertices of given degree in (general or 2-connected) random planar maps satisfies a central limit theorem with mean and variance that are asymptotically linear in the number of edges. The proof relies on an analytic version of the quadratic method and singularity analysis...

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Veröffentlicht in:Algorithmica 2013-08, Vol.66 (4), p.741-761
Hauptverfasser: Drmota, Michael, Panagiotou, Konstantinos
Format: Artikel
Sprache:eng
Schlagworte:
Algorithm Analysis and Problem Complexity
Algorithms
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Mathematics of Computing
Theory of Computation
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Zusammenfassung:We prove that the number of vertices of given degree in (general or 2-connected) random planar maps satisfies a central limit theorem with mean and variance that are asymptotically linear in the number of edges. The proof relies on an analytic version of the quadratic method and singularity analysis of multivariate generating functions.
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-013-9751-x