Zobrazeno 1 - 10
of 53
pro vyhledávání: '"Albenque, Marie"'
Publikováno v:
35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 302, pp. 6:1-6:14
We introduce a model of tree-rooted planar maps weighted by their number of $2$-connected blocks. We study its enumerative properties and prove that it undergoes a phase transition. We give the distribution of the size of the largest $2$-connected bl
Externí odkaz:
http://arxiv.org/abs/2407.16809
The Horton-Strahler number of a rooted tree $T$ is the height of the tallest complete binary tree that can be homeomorphically embedded in $T$. The number of full binary trees with $n$ internal vertices and Horton-Strahler number $s$ is known to be t
Externí odkaz:
http://arxiv.org/abs/2406.03025
Publikováno v:
Electron. J. Probab. 28, 1-54, (2023)
In this paper, the scaling limit of random connected cubic planar graphs (respectively multigraphs) is shown to be the Brownian sphere. The proof consists in essentially two main steps. First, thanks to the known decomposition of cubic planar graphs
Externí odkaz:
http://arxiv.org/abs/2203.17245
Autor:
Albenque, Marie, Ménard, Laurent
We investigate the geometry of a typical spin cluster in random triangulations sampled with a probability proportional to the energy of an Ising configuration on their vertices, both in the finite and infinite volume settings. This model is known to
Externí odkaz:
http://arxiv.org/abs/2201.11922
Combinatorial proof for the rationality of the bivariate generating series of maps in positive genus
Autor:
Albenque, Marie, Lepoutre, Mathias
In this paper, we give the first combinatorial proof of a rationality scheme for the generating series of maps in positive genus enumerated by both vertices and faces, which was first obtained by Bender, Canfield and Richmond in 1993 by purely comput
Externí odkaz:
http://arxiv.org/abs/2007.07692
We prove that random triangulations of types I, II, and III with a simple boundary under the critical Boltzmann weight converge in the scaling limit to the Brownian disk. The proof uses a bijection due to Poulalhon and Schaeffer between type III tria
Externí odkaz:
http://arxiv.org/abs/1910.04946
Autor:
Addario-Berry, Louigi, Albenque, Marie
Fix $p\geq 5$ an odd integer integer. Let $M_n$ be a uniform $p$-angulation with $n$ vertices and endowed with the uniform probability measure on its vertices. We prove that, there exists $C_p\in \mathbb{R}_+$ such that, after rescaling distances by
Externí odkaz:
http://arxiv.org/abs/1904.04786
We prove the existence of the local weak limit of the measure obtained by sampling random triangulations of size $n$ decorated by an Ising configuration with a weight proportional to the energy of this configuration. To do so, we establish the algebr
Externí odkaz:
http://arxiv.org/abs/1812.03140
In this note, we provide a new characterization of Aldous' Brownian continuum random tree as the unique fixed point of a certain natural operation on continuum trees (which gives rise to a recursive distributional equation). We also show that this fi
Externí odkaz:
http://arxiv.org/abs/1504.05445
Autor:
Albenque, Marie, Knauer, Kolja
We prove that the combinatorial optimization problem of determining the hull number of a partial cube is NP-complete. This makes partial cubes the minimal graph class for which NP-completeness of this problem is known and improves some earlier result
Externí odkaz:
http://arxiv.org/abs/1309.5724