3 citations · 5 across the 3 of their papers we have counts for
10 papers
The skeleton-blocks decomposition of Bienaymé trees, and applications to their local convergence
Marc Bernard, Robin Stephenson
We study multi-type critical Bienaymé trees through the lens of the skeleton-blocks structure, seeing them as a monotype skeleton on which we have added multi-type blocks. This dec…
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…
Scaling limits of multi-type Markov Branching trees
Bénédicte Haas, Robin Stephenson
We introduce multi-type Markov Branching trees, which are simple random population tree models where individuals are characterized by their size and type and give rise to (size,typ…
The scaling limit of a critical random directed graph
Christina Goldschmidt, Robin Stephenson
We consider the random directed graph with vertex set in which each of the possible directed edges is present independently with probabil…
On the exponential functional of Markov Additive Processes, and applications to multi-type self-similar fragmentation processes and trees
Robin Stephenson
A Markov Additive Process is a bi-variate Markov process which should be thought of as a multi-type Lévy process: the second component is a M…
Bivariate Markov chains converging to Lamperti transform Markov Additive Processes
Bénédicte Haas, Robin Stephenson
Motivated by various applications, we describe the scaling limits of bivariate Markov chains on where can be viewed as a position ma…
Local explosion in self-similar growth-fragmentation processes
Jean Bertoin, Robin Stephenson
Markovian growth-fragmentation processes describe a family of particles which can grow larger or smaller with time, and occasionally split in a conservative manner. They were intro…
Local convergence of large critical multi-type Galton-Watson trees and applications to random maps
Robin Stephenson
We show that large critical multi-type Galton-Watson trees, when conditioned to be large, converge locally in distribution to an infinite tree which is analoguous to Kesten's infin…
Scaling limits of k-ary growing trees
Bénédicte Haas, Robin Stephenson
For each integer , we introduce a sequence of -ary discrete trees constructed recursively by choosing at each step an edge uniformly among the present edges and grafti…
General Fragmentation Trees
Robin Stephenson
We show that the genealogy of any self-similar fragmentation process can be encoded in a compact measured real tree. Under some Malthusian hypotheses, we compute the fractal Hausdo…