68 citations · 297 across the 23 of their papers we have counts for
30 papers
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…
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…
Coupling Bertoin's and Aldous-Pitman's representations of the additive coalescent
Igor Kortchemski, Paul Thévenin
We construct a coupling between two seemingly very different constructions of the standard additive coalescent, which describes the evolution of masses merging pairwise at rates pr…
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…
On conditioning a self-similar growth-fragmentation by its intrinsic area
Jean Bertoin, Nicolas Curien, Igor Kortchemski
The genealogical structure of self-similar growth-fragmentations can be described in terms of a branching random walk. The so-called intrinsic area arises in this sett…
Trajectories in random minimal transposition factorizations
Valentin Féray, Igor Kortchemski
We study random typical minimal factorizations of the -cycle, which are factorizations of as a product of transpositions, chosen uniformly at random. Our m…
Condensation in critical Cauchy Bienaymé-Galton-Watson trees
Igor Kortchemski, Loïc Richier
We are interested in the structure of large Bienaymé-Galton-Watson random trees whose offspring distribution is critical and falls within the domain of attraction of a stable law o…
The boundary of random planar maps via looptrees
Igor Kortchemski, Loïc Richier
We study the scaling limits of looptrees associated with Bienaymé--Galton--Watson (BGW) trees, that are obtained by replacing every vertex of the tree by a "cycle" whose size is it…
The geometry of random minimal factorizations of a long cycle via biconditioned bitype random trees
Valentin Féray, Igor Kortchemski
We study random typical minimal factorizations of the -cycle into transpositions, which are factorizations of as a product of transpositions. By viewing tr…
Martingales in self-similar growth-fragmentations and their connections with random planar maps
Jean Bertoin, Timothy Budd, Nicolas Curien +1
The purpose of the present work is twofold. First, we develop the theory of general self-similar growth-fragmentation processes by focusing on martingales which appear naturally in…
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…
Random planar maps & growth-fragmentations
Jean Bertoin, Nicolas Curien, Igor Kortchemski
We are interested in the cycles obtained by slicing at all heights random Boltzmann triangulations with a simple boundary. We establish a functional invariance principle for the le…
Sub-exponential tail bounds for conditioned stable Bienaymé-Galton-Watson trees
Igor Kortchemski
We establish uniform sub-exponential tail bounds for the width, height and maximal outdegree of critical Bienaymé-Galton-Watson trees conditioned on having a large fixed size, whos…
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…
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.
Self-similar scaling limits of Markov chains on the positive integers
Jean Bertoin, Igor Kortchemski
We are interested in the asymptotic behavior of Markov chains on the set of positive integers for which, loosely speaking, large jumps are rare and occur at a rate that behaves lik…
Scaling limits and influence of the seed graph in preferential attachment trees
Nicolas Curien, Thomas Duquesne, Igor Kortchemski +1
We are interested in the asymptotics of random trees built by linear preferential attachment, also known in the literature as Barabási-Albert trees or plane-oriented recursive tree…
A predator-prey SIR type dynamics on large complete graphs with three phase transitions
Igor Kortchemski
We are interested in a variation of the SIR (Susceptible/Infected/Recovered) dynamics on the complete graph, in which infected individuals may only spread to neighboring susceptibl…
Predator-prey dynamics on infinite trees: a branching random walk approach
Igor Kortchemski
We are interested in predator-prey dynamics on infinite trees, which can informally be seen as particular two-type branching processes where individuals may die (or be infected) on…
Percolation on random triangulations and stable looptrees
Nicolas Curien, Igor Kortchemski
We study site percolation on Angel & Schramm's uniform infinite planar triangulation. We compute several critical and near-critical exponents, and describe the scaling limit of the…
The CRT is the scaling limit of random dissections
Nicolas Curien, Bénédicte Haas, Igor Kortchemski
We study the graph structure of large random dissections of polygons sampled according to Boltzmann weights, which encompasses the case of uniform dissections or uniform -angula…
Random stable looptrees
Nicolas Curien, Igor Kortchemski
We introduce a class of random compact metric spaces L(α) indexed by α\in (1,2) and which we call stable looptrees. They are made of a collection of random loops glued together alo…