12 papers
The conformally invariant metric on CLE III: uniqueness
Emmanuel Kammerer, Konstantinos Kavvadias, Jason Miller +1
This paper is the third and final article in a series of papers constructing the canonical conformally invariant metric on the set of loops of the conformal loop ensemble (CLE) wit…
The conformally invariant metric on CLE II: existence of geodesics
Emmanuel Kammerer, Konstantinos Kavvadias, Jason Miller +1
We continue our study of the conformal loop ensemble (CLE) with parameter , the critical threshold at or below which the loops are simple and disjoint, touching neither each o…
The conformally invariant metric on CLE I: subsequential limits of the non-simple CLE graph metric
Emmanuel Kammerer, Konstantinos Kavvadias, Jason Miller +1
We consider the conformal loop ensemble (CLE) with the parameter , the critical value at or below which the loops are simple and do not intersect each other or the domain boun…
From Kreweras walks to branching perimeter processes of percolated triangulations
Renan Gross, Emmanuel Kammerer, Frederik Ravn Klausen
In this note, using a result of Bernardi, Holden and Sun, we give an explicit geometric relation between the perimeter of the peeling process along the percolation interface of a t…
Depth profile of depth-weighted trees with bounded weights
Emmanuel Kammerer
We study the depth-weighted random recursive trees introduced by Leckey, Mitsche and Wormald in the case where the weights are bounded from above and from below. We establish the s…
The height of the infection tree
Emmanuel Kammerer, Igor Kortchemski, Delphin Sénizergues
We are interested in the geometry of the ``infection tree'' in a stochastic SIR (Susceptible-Infectious-Recovered) model, starting with a single infectious individual. This tree is…
Gaskets of loop-decorated random planar maps
Emmanuel Kammerer
We prove that for the gaskets of critical rigid loop-decorated random planar maps are -stable maps. The case thus corresponds to the critical case in ra…
Scaling limit of trees with vertices of fixed degrees and heights
Arthur Blanc-Renaudie, Emmanuel Kammerer
We consider large uniform random trees where we fix for each vertex its degree and height. We prove, under natural conditions of convergence for the profile, that those trees prope…
Distances on the , critical Liouville quantum gravity and -stable maps
Emmanuel Kammerer
The purpose of this article is threefold. First, we show that when one explores a conformal loop ensemble of parameter () on an independent -Liouville quan…
Uniform attachment with freezing
Étienne Bellin, Arthur Blanc-Renaudie, Emmanuel Kammerer +1
In the classical model of random recursive trees, trees are recursively built by attaching new vertices to old ones. What happens if vertices are allowed to freeze, in the sense th…
Uniform attachment with freezing: Scaling limits
Étienne Bellin, Arthur Blanc-Renaudie, Emmanuel Kammerer +1
We investigate scaling limits of trees built by uniform attachment with freezing, which is a variant of the classical model of random recursive trees introduced in a companion pape…
On large -stable maps
Emmanuel Kammerer
We discuss asymptotics of large Boltzmann random planar maps such that every vertex of degree has weight of order . Infinite maps of that kind were studied by Budd, Cur…