11 papers
The isomorphism problem for random generalized Baumslag-Solitar groups with many edges
Dario Ascari, Alessandra Caraceni
The isomorphism problem for generalized Baumslag-Solitar (GBS) groups is a long-standing open problem. We prove that, in the random model considered here, a GBS graph with many edg…
Sweet Trims are made of Threes: A càdlàg erasure of the Brownian tree
Alessandra Caraceni, Nicolas Curien, William Fleurat +1
We present a simple trimming algorithm that generates nested uniform binary plane trees by removing leaves one-by-one using a best-of-three-match procedure. While its one-step tran…
A Proof of the Symmetric Theta Conjecture when q = 0
Alessandra Caraceni, Alessandro Iraci
In 10.1093/imrn/rnac258, the authors conjecture a combinatorial formula for the expressions , known as Symmetric Theta Trees Conjecture, in terms of tiered trees…
Where do (random) trees grow leaves?
Alessandra Caraceni, Nicolas Curien, Robin Stephenson
We study a model of random binary trees grown "by the leaves" in the style of Luczak and Winkler. If is a uniform plane binary tree of size , Luczak and Winkler, and later…
Growing uniform planar maps face by face
Alessandra Caraceni, Alexandre Stauffer
We provide "growth schemes" for inductively generating uniform random -angulations of the sphere with faces, as well as uniform random simple triangulations of the sphere w…
Bijections for Ranked Tree-Child Networks
Alessandra Caraceni, Michael Fuchs, Guan-Ru Yu
The class of ranked tree-child networks, tree-child networks arising from an evolution process with a fixed embedding into the plane, has recently been introduced by Bienvenu, Lamb…
A polynomial upper bound for the mixing time of edge rotations on planar maps
Alessandra Caraceni
We consider a natural local dynamic on the set of all rooted planar maps with edges that is in some sense analogous to "edge flip" Markov chains, which have been considered bef…
Polynomial mixing time of edge flips on quadrangulations
Alessandra Caraceni, Alexandre Stauffer
We establish the first polynomial upper bound for the mixing time of random edge flips on rooted quadrangulations: we show that the spectral gap of the edge flip Markov chain on qu…
Self-Avoiding Walks on the UIPQ
Alessandra Caraceni, Nicolas Curien
We study an annealed model of Uniform Infinite Planar Quadrangulation (UIPQ) with an infinite two-sided self-avoiding walk (SAW), which can also be described as the result of gluei…
Geometry of the Uniform Infinite Half-Planar Quadrangulation
Alessandra Caraceni, Nicolas Curien
We give a new construction of the uniform infinite half-planar quadrangulation with a general boundary (or UIHPQ), analogous to the construction of the UIPQ presented by Chassaing…
The Scaling Limit of Random Outerplanar Maps
Alessandra Caraceni
A planar map is outerplanar if all its vertices belong to the same face. We show that random uniform outerplanar maps with vertices suitably rescaled by a factor …