Collet, G., Drmota, M., & Klausner, L. D. (2019). Limit laws of planar maps with prescribed vertex degrees. Combinatorics, Probability and Computing, 28(4), 519–541. https://doi.org/10.1017/s0963548318000573
E104-01 - Forschungsbereich Algebra E104-05 - Forschungsbereich Kombinatorik und Algorithmen
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Journal:
Combinatorics, Probability and Computing
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ISSN:
0963-5483
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Date (published):
2019
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Number of Pages:
23
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Peer reviewed:
Yes
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Keywords:
Applied Mathematics; Theoretical Computer Science; Computational Theory and Mathematics; Statistics and Probability
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Abstract:
We prove a generalmulti-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 possible extensions to maps of higher genus and to weighted maps.
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Research Areas:
außerhalb der gesamtuniversitären Forschungsschwerpunkte: 100%
