Collet, G., Drmota, M., & Klausner, L. (2016). Vertex Degrees in Planar Maps. In M. Zaionc & R. Neininger (Eds.), Proceedings of the 27th International Conference on Probalistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms. AofA. https://doi.org/10.48550/arXiv.1605.04206
E104-01 - Forschungsbereich Algebra E104-05 - Forschungsbereich Kombinatorik und Algorithmen
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Published in:
Proceedings of the 27th International Conference on Probalistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms
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Date (published):
2016
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Event name:
AofA'16
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Event date:
4-Jul-2016 - 8-Jul-2016
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Event place:
Krakau, Poland
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Number of Pages:
16
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Publisher:
AofA, Krakow, Polen
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Keywords:
Analytic Combinatorics; Planar Maps; Central Limit Theorem; Mobiles
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Abstract:
We prove a general multi-dimensional central limit theorem for the expected number of vertices of a given degree in the family of planar maps whose vertex degrees are restricted to an arbitrary (finite or infinite) set of positive integers D. Our results rely on a classical bijection with mobiles (objects exhibiting a tree structure), combined with refined analytic tools to deal with the systems of equations on infinite variables that arise. We also discuss some possible extension to maps of higher genus.