29 citations · 136 across the 18 of their papers we have counts for
18 papers
Rémy's diffusion on Brownian trees
Nicolas Curien, Cyril Marzouk
Rémy's algorithm is a famous recursive construction of uniform random binary trees of growing size by a local grafting operation. In this work we construct a continuous version, a…
Random Lévy Looptrees and Lévy Maps
Igor Kortchemski, Cyril Marzouk
What is the analogue of Lévy processes for random surfaces? Motivated by scaling limits of random planar maps in random geometry, we introduce and study Lévy looptrees and Lévy map…
Scaling limits of random looptrees and bipartite plane maps with prescribed large faces
Cyril Marzouk
We first rephrase and unify known bijections between bipartite plane maps and labelled trees with the formalism of looptrees, which we argue to be both more relevant and technicall…
The mesoscopic geometry of sparse random maps
Nicolas Curien, Igor Kortchemski, Cyril Marzouk
We investigate the structure of large uniform random maps with edges, faces, and with genus in the so-called sparse case, where the ratio between…
Large deviation Local Limit Theorems and limits of biconditioned Trees and Maps
Igor Kortchemski, Cyril Marzouk
We first establish new local limit estimates for the probability that a nondecreasing integer-valued random walk lies at time at an arbitrary value, encompassing in particular…
Infinite stable Boltzmann planar maps are subdiffusive
Nicolas Curien, Cyril Marzouk
The infinite discrete stable Boltzmann maps are generalisations of the well-known Uniform Infinite Planar Quadrangulation in the case where large degree faces are allowed. We show…
On scaling limits of random trees and maps with a prescribed degree sequence
Cyril Marzouk
We study a configuration model on bipartite planar maps in which, given even integers, one samples a planar map with faces uniformly at random with these face degrees. We p…
Markovian explorations of random planar maps are roundish
Nicolas Curien, Cyril Marzouk
The infinite discrete stable Boltzmann maps are "heavy-tailed" generalisations of the well-known Uniform Infinite Planar Quadrangulation. Very efficient tools to study these object…
On the growth of random planar maps with a prescribed degree sequence
Cyril Marzouk
For non-negative integers such that , we sample a bipartite planar map with faces uniformly at random amongst those which have $…
On scaling limits of planar maps with stable face-degrees
Cyril Marzouk
We discuss the asymptotic behaviour of random critical Boltzmann planar maps in which the degree of a typical face belongs to the domain of attraction of a stable law with index $α…
How fast planar maps get swallowed by a peeling process
Nicolas Curien, Cyril Marzouk
The peeling process is an algorithmic procedure that discovers a random planar map step by step. In generic cases such as the UIPT or the UIPQ, it is known [Curien & Le Gall, Scali…
Scaling limits of discrete snakes with stable branching
Cyril Marzouk
We consider so-called discrete snakes obtained from size-conditioned critical Bienaymé-Galton-Watson trees by assigning to each node a random spatial position in such a way that th…
Infinite random planar maps related to Cauchy processes
Timothy Budd, Nicolas Curien, Cyril Marzouk
We study the geometry of infinite random Boltzmann planar maps having weight of polynomial decay of order for each vertex of degree . These correspond to the dual of th…
Scaling limits of random bipartite planar maps with a prescribed degree sequence
Cyril Marzouk
We study the asymptotic behaviour of uniform random maps with a prescribed face-degree sequence, in the bipartite case, as the number of faces tends to infinity. Under mild assumpt…
Triangulating stable laminations
Igor Kortchemski, Cyril Marzouk
We study the asymptotic behavior of random simply generated noncrossing planar trees in the space of compact subsets of the unit disk, equipped with the Hausdorff distance. Their d…
Simply generated non-crossing partitions
Igor Kortchemski, Cyril Marzouk
We introduce and study the model of simply generated non-crossing partitions, which are, roughly speaking, chosen at random according to a sequence of weights. This framework encom…
Fires on large recursive trees
Cyril Marzouk
We consider random dynamics on a uniform random recursive tree with vertices. Successively, in a uniform random order, each edge is either set on fire with some probability $p_…
On the sizes of burnt and fireproof components for fires on a large Cayley tree
Cyril Marzouk
We continue the study initiated by Jean Bertoin in 2012 of a random dynamics on the edges of a uniform Cayley tree with vertices in which, successively, each edge is either set…