2 Search Results for "Hwang, Hsien-Kuei"


Document
Asymptotic Distribution of Parameters in Random Maps

Authors: Olivier Bodini, Julien Courtiel, Sergey Dovgal, and Hsien-Kuei Hwang

Published in: LIPIcs, Volume 110, 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)


Abstract
We consider random rooted maps without regard to their genus, with fixed large number of edges, and address the problem of limiting distributions for six different parameters: vertices, leaves, loops, root edges, root isthmus, and root vertex degree. Each of these leads to a different limiting distribution, varying from (discrete) geometric and Poisson distributions to different continuous ones: Beta, normal, uniform, and an unusual distribution whose moments are characterised by a recursive triangular array.

Cite as

Olivier Bodini, Julien Courtiel, Sergey Dovgal, and Hsien-Kuei Hwang. Asymptotic Distribution of Parameters in Random Maps. In 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 110, pp. 13:1-13:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{bodini_et_al:LIPIcs.AofA.2018.13,
  author =	{Bodini, Olivier and Courtiel, Julien and Dovgal, Sergey and Hwang, Hsien-Kuei},
  title =	{{Asymptotic Distribution of Parameters in Random Maps}},
  booktitle =	{29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)},
  pages =	{13:1--13:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-078-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{110},
  editor =	{Fill, James Allen and Ward, Mark Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2018.13},
  URN =		{urn:nbn:de:0030-drops-89069},
  doi =		{10.4230/LIPIcs.AofA.2018.13},
  annote =	{Keywords: Random maps, Analytic combinatorics, Rooted Maps, Beta law, Limit laws, Patterns, Generating functions, Riccati equation}
}
Document
Asymptotic Expansions for Sub-Critical Lagrangean Forms

Authors: Hsien-Kuei Hwang, Mihyun Kang, and Guan-Huei Duh

Published in: LIPIcs, Volume 110, 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)


Abstract
Asymptotic expansions for the Taylor coefficients of the Lagrangean form phi(z)=zf(phi(z)) are examined with a focus on the calculations of the asymptotic coefficients. The expansions are simple and useful, and we discuss their use in some enumerating sequences in trees, lattice paths and planar maps.

Cite as

Hsien-Kuei Hwang, Mihyun Kang, and Guan-Huei Duh. Asymptotic Expansions for Sub-Critical Lagrangean Forms. In 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 110, pp. 29:1-29:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Copy BibTex To Clipboard

@InProceedings{hwang_et_al:LIPIcs.AofA.2018.29,
  author =	{Hwang, Hsien-Kuei and Kang, Mihyun and Duh, Guan-Huei},
  title =	{{Asymptotic Expansions for Sub-Critical Lagrangean Forms}},
  booktitle =	{29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)},
  pages =	{29:1--29:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-078-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{110},
  editor =	{Fill, James Allen and Ward, Mark Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2018.29},
  URN =		{urn:nbn:de:0030-drops-89224},
  doi =		{10.4230/LIPIcs.AofA.2018.29},
  annote =	{Keywords: asymptotic expansions, Lagrangean forms, saddle-point method, singularity analysis, maps}
}
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