We study random cutting down of a rooted tree and show that the number of cuts is equal (in distribution) to the number of records in the tree when edges (or vertices) are assigned random labels. Limi...
We study a queueing system with Poisson arrivals on a bus line indexed by integers. The buses move at constant speed to the right, and the time of service per customer getting on the bus is fixed. The...
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 analogous to Kesten’s infinite monotype Galton–W...
We investigate a simple quantitative genetics model subjet to a gradual environmental change from the viewpoint of the phylogenies of the living individuals. We aim to understand better how the past t...
We introduce a random finite rooted tree $\mathcal{C}$, the steady state cluster, characterized by a recursive description: $\mathcal{C}$ is a singleton with probability $1/2$ and otherwise is obtaine...
We give a unified treatment of the limit, as the size tends to infinity, of simply generated random trees, including both the well-known result in the standard case of critical Galton–Watson trees...
We extend the infinite-allele simple branching process of Griffiths and Pakes (1988) allowing the offspring to change types and labels. The model is developed and limit theorems are given for the grow...
We describe and study the delayed multi-type branching process, a finite-time delayed multi-type branching process in which individuals are active (can reproduce offspring) during a finite time interv...
We consider the ferromagnetic Ising model on a sequence of graphs $G_n$ converging locally weakly to a rooted random tree. Generalizing [Montanari, Mossel, Sly '11], under an appropriate "continuity" ...
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continu...
We consider distributional fixed point equations of the form X D = ∨iTiXi in a systematic way. The distribution of T = (T1, T2, . . .) is given in advance. The positive rvs T,Xi, i ∈ IN are independen...
We consider branching processes in discrete time for structured population in varying environment. Each individual has a trait which belongs to some general state space and both its reproduction law a...
We consider Markov jump processes describing structured populations with interactions via density dependance. We propose a Markov construction with a distinguished individual which allows to describe ...
Using an associated branching process as the basis of our approximation, we show that typical inter-point distances in a multi-type random intersection graph have a defective distribution, which is we...
This paper is centered on covariant dynamics on unimodular random graphs and random networks, namely maps from the set of vertices to itself which are preserved by graph or network isomorphisms. Such ...
The notion of information pervades informal descriptions of biological systems, but formal treatments face the problem of defining a quantitative measure of information rooted in a concept of fitness,...
The Kesten-Stigum theorem for the one-type Galton-Watson process gives necessary and sufficient conditions for mean convergence of the martingale formed by the population size normed by its expectatio...
It is conjectured in the Physics literature that properly rescaled random planar maps, when conditioned to have a large number of faces, should converge to a limiting surface whose law does not depend...
In this paper, we provide a pathwise spine decomposition for superprocesses with both local and non-local branching mechanisms under a martingale change of measure. This result complements the related...
In the present paper, we study the evolution of an overloaded cyclic polling model that starts empty. Exploiting a connection with multitype branching processes, we derive fluid asymptotics for the jo...