Record link: 
http://hdl.handle.net/20.500.12708/41489
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Title: 
Vertex Degrees in Planar Maps
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Citation: 
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
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Publisher DOI: 
10.48550/arXiv.1605.04206
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Publication Type: 
Inproceedings - Full-Paper Contribution
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Language: 
English
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Authors: 
Collet, Gwendal 
Drmota, Michael 
Klausner, Lukas 
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Organisational Unit: 
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.
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Science Branch: 
Mathematik
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Appears in Collections:
Conference Paper

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