6 papers
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…
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…