Random cubic planar maps

We analyse uniform random cubic rooted planar maps and obtain limiting distributions for several parameters of interest. From the enumerative point of view, we present a unified approach for the enumeration of several classes of cubic planar maps, which allow us to recover known results in a more ge...

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Autores: Drmota, Michael, Noy Serrano, Marcos|||0000-0002-2399-1359, Requile, Clement|||0000-0002-7689-7972, Rué Perna, Juan José|||0000-0002-6420-3179
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/395379
Acceso en línea:https://hdl.handle.net/2117/395379
https://dx.doi.org/10.37236/11619
Access Level:acceso abierto
Palabra clave:Graph theory
enumerative combinatorics
analytic combinatorics
map enumeration
Grafs, Teoria de
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
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repository_id_str
spelling Random cubic planar mapsDrmota, MichaelNoy Serrano, Marcos|||0000-0002-2399-1359Requile, Clement|||0000-0002-7689-7972Rué Perna, Juan José|||0000-0002-6420-3179Graph theoryenumerative combinatoricsanalytic combinatoricsmap enumerationGrafs, Teoria deClassificació AMS::05 Combinatorics::05C Graph theoryÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafsWe analyse uniform random cubic rooted planar maps and obtain limiting distributions for several parameters of interest. From the enumerative point of view, we present a unified approach for the enumeration of several classes of cubic planar maps, which allow us to recover known results in a more general and transparent way. This approach allows us to obtain new enumerative results. Concerning random maps, we first obtain the distribution of the degree of the root face, which has an exponential tail as for other classes of random maps. Our main result is a limiting map-Airy distribution law for the size of the largest block L, whose expectation is asymptotically n/v3 in a random cubic map with n+ 2 faces. We prove analogous results for the size of the largest cubic block, obtained from L by erasing all vertices of degree two, and for the size of the largest 3-connected component, whose expected values are respectively n/2 and n/4. To obtain these results we need to analyse a new type of composition scheme which has not been treated by Banderier et al. [Random Structures Algorithms 2001].Peer Reviewed20232023-06-3020232023-10-25journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/395379https://dx.doi.org/10.37236/11619reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengAgencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016 MTM2017-82166-P COMBINATORIA GEOMETRICA, ALGEBRAICA Y PROBABILISTICAAgencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-113082GB-I00 COMBINATORIA: NUEVAS TENDENCIAS Y APLICACIONESopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3953792026-05-27T15:37:01Z
dc.title.none.fl_str_mv Random cubic planar maps
title Random cubic planar maps
spellingShingle Random cubic planar maps
Drmota, Michael
Graph theory
enumerative combinatorics
analytic combinatorics
map enumeration
Grafs, Teoria de
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
title_short Random cubic planar maps
title_full Random cubic planar maps
title_fullStr Random cubic planar maps
title_full_unstemmed Random cubic planar maps
title_sort Random cubic planar maps
dc.creator.none.fl_str_mv Drmota, Michael
Noy Serrano, Marcos|||0000-0002-2399-1359
Requile, Clement|||0000-0002-7689-7972
Rué Perna, Juan José|||0000-0002-6420-3179
author Drmota, Michael
author_facet Drmota, Michael
Noy Serrano, Marcos|||0000-0002-2399-1359
Requile, Clement|||0000-0002-7689-7972
Rué Perna, Juan José|||0000-0002-6420-3179
author_role author
author2 Noy Serrano, Marcos|||0000-0002-2399-1359
Requile, Clement|||0000-0002-7689-7972
Rué Perna, Juan José|||0000-0002-6420-3179
author2_role author
author
author
dc.subject.none.fl_str_mv Graph theory
enumerative combinatorics
analytic combinatorics
map enumeration
Grafs, Teoria de
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
topic Graph theory
enumerative combinatorics
analytic combinatorics
map enumeration
Grafs, Teoria de
Classificació AMS::05 Combinatorics::05C Graph theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
description We analyse uniform random cubic rooted planar maps and obtain limiting distributions for several parameters of interest. From the enumerative point of view, we present a unified approach for the enumeration of several classes of cubic planar maps, which allow us to recover known results in a more general and transparent way. This approach allows us to obtain new enumerative results. Concerning random maps, we first obtain the distribution of the degree of the root face, which has an exponential tail as for other classes of random maps. Our main result is a limiting map-Airy distribution law for the size of the largest block L, whose expectation is asymptotically n/v3 in a random cubic map with n+ 2 faces. We prove analogous results for the size of the largest cubic block, obtained from L by erasing all vertices of degree two, and for the size of the largest 3-connected component, whose expected values are respectively n/2 and n/4. To obtain these results we need to analyse a new type of composition scheme which has not been treated by Banderier et al. [Random Structures Algorithms 2001].
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-06-30
2023
2023-10-25
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/395379
https://dx.doi.org/10.37236/11619
url https://hdl.handle.net/2117/395379
https://dx.doi.org/10.37236/11619
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016 MTM2017-82166-P COMBINATORIA GEOMETRICA, ALGEBRAICA Y PROBABILISTICA
Agencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-113082GB-I00 COMBINATORIA: NUEVAS TENDENCIAS Y APLICACIONES
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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