Abstract
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.
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Notes
This proof is not included in the final version of the proceedings paper [8].
As in previous case the same approach applies if the functions \(\overline{G}_{i}\) depend on y(z,x,w), too.
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The first author is supported by the Austrian Science Foundation FWF, Project S9604. The second author is supported by the German Research Foundation, Grant PA 2080/2-1. An extended abstract of this work appeared in the Proceedings of the Meeting on Analytic Algorithmics and Combinatorics (ANALCO12), 2012.
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Drmota, M., Panagiotou, K. A Central Limit Theorem for the Number of Degree-k Vertices in Random Maps. Algorithmica 66, 741–761 (2013). https://doi.org/10.1007/s00453-013-9751-x
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DOI: https://doi.org/10.1007/s00453-013-9751-x