dc.contributor.author |
Drmota, M. |
dc.contributor.author |
Noy, M. |
dc.contributor.author |
Requilé, C. |
dc.contributor.author |
Rué, J. |
dc.date.accessioned |
2023-07-03T07:41:02Z |
dc.date.available |
2023-07-03T07:41:02Z |
dc.date.issued |
2023-06-30 |
dc.identifier.uri |
http://hdl.handle.net/2072/535957 |
dc.description.sponsorship |
Supported by the Special Research Program SFB F50-02Algorithmic and Enumerative Combina-torics, and by the project P35016Infinite Singular Systems and Random Discrete Objectsof the AustrianScience Fund FWF.†Supported by grants MTM2017-82166-P and PID2020-113082GB-I00, and the Severo Ochoa andMar ́ıa de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M).‡Supported by the grant Beatriu de Pin ́os BP2019, funded by the H2020 COFUND project No 801370and AGAUR (the Catalan agency for management of university and research grants), and the grantPID2020-113082GB-I00 of the Spanish ministry of Science and Innovation |
dc.format.extent |
41 p. |
dc.language.iso |
eng |
dc.publisher |
Electronic Journal of Combinatronics |
dc.relation.ispartof |
The Electronic Journal of Combinatronics |
dc.rights |
L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: http://creativecommons.org/licenses/by-nd/4.0/ |
dc.source |
RECERCAT (Dipòsit de la Recerca de Catalunya) |
dc.subject.other |
Cubic planar maps, Combinatronics |
dc.title |
Random Cubic Planar Maps |
dc.type |
info:eu-repo/semantics/article |
dc.type |
info:eu-repo/semantics/publishedVersion |
dc.embargo.terms |
cap |
dc.identifier.doi |
10.37236/11619 |
dc.rights.accessLevel |
info:eu-repo/semantics/openAccess |
dc.description.abstract |
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 / √ 3 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]. |