Limit Laws of Planar Maps with Prescribed Vertex Degrees

Autor: Collet, Gwendal, Drmota, Michael, Klausner, Lukas Daniel

Publikováno v: Comb. Probab. Comput. 28 (4) (Special Issue on Analysis of Algorithms), 2019, 519-541

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 r

Externí odkaz: http://arxiv.org/abs/1808.05944

Threshold functions for small subgraphs: an analytic approach

Autor: Collet, Gwendal, de Panafieu, Élie, Gardy, Danièle, Gittenberger, Bernhard, Ravelomanana, Vlady

We revisit the problem of counting the number of copies of a fixed graph in a random graph or multigraph, including the case of constrained degrees. Our approach relies heavily on analytic combinatorics and on the notion of patchwork to describe the

Externí odkaz: http://arxiv.org/abs/1705.08768

Random maps: proceeding of the Journ{\'e}es MAS 2014

Autor: Abraham, Céline, Bettinelli, Jérémie, Collet, Gwendal, Kortchemski, Igor

This is a quick survey on some recent works done in the field of random maps.
Comment: arXiv admin note: text overlap with arXiv:1307.6818

Externí odkaz: http://arxiv.org/abs/1412.1610

A simple formula for the series of constellations and quasi-constellations with boundaries

Autor: Collet, Gwendal, Fusy, Eric

We obtain a very simple formula for the generating function of bipartite (resp. quasi-bipartite) planar maps with boundaries (holes) of prescribed lengths, which generalizes certain expressions obtained by Eynard in a book to appear. The formula is d

Externí odkaz: http://arxiv.org/abs/1205.5215

Random maps

Autor: Abraham, Céline, Bettinelli, Jérémie, Collet, Gwendal, Kortchemski, Igor, Garivier, Aurélien

Publikováno v: Modélisation aléatoire et statistique-Journées MAS 2014
Journées MAS 2014
Journées MAS 2014, Aug 2014, Toulouse, France. pp.133--149, ⟨10.1051/proc/201551008⟩
ESAIM: Proceedings and Surveys, Vol 51, Pp 133-149 (2015)

This is a quick survey on some recent works done in the field of random maps, which, very roughly speaking, are graphs embedded without edge crossings in a surface. We present the main results and tools in this area then summarize the original contri

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b7ffa02c423610de35b024197fae19f4
https://hal.archives-ouvertes.fr/hal-01090666