Add to ORKGWe discuss scaling limits of random planar maps chosen uniformly over the set of all 2p-angulations with n faces. This leads to a limiting space called the Brownian map, which is viewed as a random compact metric space. Although we are not able to prove the uniqueness of the distribution of the Brownian map, many of its properties can be investigated in detail. In particular, we obtain a complete description of the geodesics starting from the distinguished point called the root. We give applications to various properties of large random planar maps
Fix an arbitrary compact orientable surface with a boundary and consider a uniform bipartite random ...
International audienceLet M-n be a simple triangulation of the sphere S-2, drawn uniformly at random...
We study a configuration model on bipartite planar maps where, given $n$ even integers, one samples ...
We discuss scaling limits of random planar maps chosen uniformly over the set of all 2p-angulations ...
76 pages, 7 figures, improved versionWe prove that uniform random quadrangulations of the sphere wit...
We prove that uniform random quadrangulations of the sphere with n faces, endowed with the usual gra...
Random planar maps are considered in the physics literature as the dis-crete counterpart of random s...
We introduce and study the random non-compact metric space called the Brownian plane, which is obtai...
Abstract We introduce and study the random non-compact metric space called the Brownian plane, which...
This thesis investigates the geometry of random spaces. Geodesics in random surfaces. The Br...
Abstract. For every integer n ≥ 1, we consider a random planar map Mn which is uniformly distributed...
Abstract. We introduce and study a universal model of random geometry in two dimen-sions. To this en...
Consider qn a random pointed quadrangulation chosen equally likely among the pointed quadrangulation...
26 pages, 4 figuresFor non-negative integers $(d_n(k))_{k \ge 1}$ such that $\sum_{k \ge 1} d_n(k) =...
A planar map is outerplanar if all its vertices belong to the same face. We show that random unifor...
Fix an arbitrary compact orientable surface with a boundary and consider a uniform bipartite random ...
International audienceLet M-n be a simple triangulation of the sphere S-2, drawn uniformly at random...
We study a configuration model on bipartite planar maps where, given $n$ even integers, one samples ...
We discuss scaling limits of random planar maps chosen uniformly over the set of all 2p-angulations ...
76 pages, 7 figures, improved versionWe prove that uniform random quadrangulations of the sphere wit...
We prove that uniform random quadrangulations of the sphere with n faces, endowed with the usual gra...
Random planar maps are considered in the physics literature as the dis-crete counterpart of random s...
We introduce and study the random non-compact metric space called the Brownian plane, which is obtai...
Abstract We introduce and study the random non-compact metric space called the Brownian plane, which...
This thesis investigates the geometry of random spaces. Geodesics in random surfaces. The Br...
Abstract. For every integer n ≥ 1, we consider a random planar map Mn which is uniformly distributed...
Abstract. We introduce and study a universal model of random geometry in two dimen-sions. To this en...
Consider qn a random pointed quadrangulation chosen equally likely among the pointed quadrangulation...
26 pages, 4 figuresFor non-negative integers $(d_n(k))_{k \ge 1}$ such that $\sum_{k \ge 1} d_n(k) =...
A planar map is outerplanar if all its vertices belong to the same face. We show that random unifor...
Fix an arbitrary compact orientable surface with a boundary and consider a uniform bipartite random ...
International audienceLet M-n be a simple triangulation of the sphere S-2, drawn uniformly at random...
We study a configuration model on bipartite planar maps where, given $n$ even integers, one samples ...