62 citations · 124 across the 15 of their papers we have counts for
11 papers · 1 filter
Compact Brownian surfaces II. Orientable surfaces
Jérémie Bettinelli, Grégory Miermont
Fix an arbitrary compact orientable surface with a boundary and consider a uniform bipartite random quadrangulation of this surface with faces and boundary component lengths of…
Scaling limit of random plane quadrangulations with a simple boundary, via restriction
Jérémie Bettinelli, Nicolas Curien, Luis Fredes +1
We prove that quadrangulations with a simple boundary converge to the Brownian disk. More precisely, we fix a sequence of even positive integers with …
Convergence of uniform noncrossing partitions toward the Brownian triangulation
Jérémie Bettinelli
We give a short proof that a uniform noncrossing partition of the regular -gon weakly converges toward Aldous's Brownian triangulation of the disk, in the sense of the Hausdorff…
Compact Brownian surfaces I. Brownian disks
Jérémie Bettinelli, Gregory Miermont
We show that, under certain natural assumptions, large random plane bipartite maps with a boundary converge after rescaling to a one-parameter family (, $0 < L < \in…
Random maps: proceeding of the Journ{é}es MAS 2014
Céline Abraham, Jérémie Bettinelli, Gwendal Collet +1
This is a quick survey on some recent works done in the field of random maps.
Geodesics in Brownian surfaces (Brownian maps)
Jérémie Bettinelli
We define a class a metric spaces we call Brownian surfaces, arising as the scaling limits of random maps on general orientable surfaces with a boundary and we study the geodesics…
The scaling limit of uniform random plane maps, via the Ambjørn-Budd bijection
Jérémie Bettinelli, Emmanuel Jacob, Grégory Miermont
We prove that a uniform rooted plane map with n edges converges in distribution after a suitable normalization to the Brownian map for the Gromov-Hausdorff topology. A recent bijec…
Increasing Forests and Quadrangulations via a Bijective Approach
Jérémie Bettinelli
In this work, we expose four bijections each allowing to increase (or decrease) one parameter in either uniform random forests with a fixed number of edges and trees, or quadrangul…
Scaling Limit of Random Planar Quadrangulations with a Boundary
Jérémie Bettinelli
We discuss the scaling limit of large planar quadrangulations with a boundary whose length is of order the square root of the number of faces. We consider a sequence of int…
The topology of scaling limits of positive genus random quadrangulations
Jérémie Bettinelli
We discuss scaling limits of large bipartite quadrangulations of positive genus. For a given g, we consider, for every , a random quadrangulation uniformly…
Scaling Limits for Random Quadrangulations of Positive Genus
Jérémie Bettinelli
We discuss scaling limits of large bipartite quadrangulations of positive genus. For a given , we consider, for every , a random quadrangulation $\q_n$ uniformly distri…