Related papers: Limit theorems for supercritical age-dependent bra…
Near the beginning of the century, Wright and Fisher devised an elegant, mathematically tractable model of gene reproduction and replacement that laid the foundation for contemporary population genetics. The Wright-Fisher model and its…
Multi-type inhomogeneous Galton--Watson process with immigration is investigated, where the offspring mean matrix slowly converges to a critical mean matrix. Under general conditions we obtain limit distribution for the process, where the…
A density-dependent branching process is a particle system in which individuals reproduce independently, but in a way that depends on the current population size. This feature can model a wide range of ecological interactions at the cost of…
We consider a (one-dimensional) branching Brownian motion process with a general offspring distribution having at least two moments, and in which all particles have a drift towards the origin where they are immediately absorbed. It is…
We consider a totally asymmetric exclusion process on the positive half-line. When particles enter in the system according to a Poisson source, Liggett has computed all the limit distributions when the initial distribution has an asymptotic…
Near critical catalyst-reactant branching processes with controlled immigration are studied. The reactant population evolves according to a branching process whose branching rate is proportional to the total mass of the catalyst. The bulk…
For any branching process, we demonstrate that the typical total number $r_{\rm mp}(\nu \tau)$ of events triggered over all generations within any sufficiently large time window $\tau$ exhibits, at criticality, a super-linear dependence…
The goal of this paper is to develop a theory of graphon-valued stochastic processes, and to construct and analyse a natural class of such processes arising from population genetics. We consider finite populations where individuals change…
We consider a general branching population where the lifetimes of individuals are i.i.d.\ with arbitrary distribution and where each individual gives birth to new individuals at Poisson times independently from each other. In addition, we…
We consider a branching random walk with immigration in a random environment, where the environment is a stationary and ergodic sequence indexed by time. We focus on the asymptotic properties of the sequence of measures $(Z_n)$ that count…
A superprocess limit for an interacting birth-death particle system modelling a population with trait and physical age-structures is established. Traits of newborn offspring are inherited from the parents except when mutations occur, while…
For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. For the subcritical regime a kind of phase transition…
In this paper, we establish a central limit theorem for a large class of general supercritical superprocesses with immigration with spatially dependent branching mechanisms satisfying a second moment condition. This central limit theorem…
For a discrete time multitype supercritical Galton-Watson process $(Z_n)_{n\in \mathbb{N}}$ and corresponding genealogical tree $\mathbb{T}$, we associate a new discrete time process $(Z_n^{\Phi})_{n\in\mathbb{N}}$ such that, for each $n\in…
In this paper we consider two branching processes living in a joint random environment. Assuming that both processes are critical we address the following question: What is the probability that both populations survive up to a large time…
Consider a population where individuals give birth at constant rate during their lifetimes to i.i.d. copies of themselves. Individuals bear clonally inherited types, but (neutral) mutations may happen at the birth events. The smallest…
Consider a branching Markov process with values in some general type space. Conditional on survival up to generation $N$, the genealogy of the extant population defines a random marked metric measure space, where individuals are marked by…
In this paper, we study a Galton-Watson process $(Z_n)$ with infinitely many types in a random ergodic environment $\bar{\xi}=(\xi_n)_{n\geq 0}$. We focus on the supercritical regime of the process, where the quenched average of the size of…
We consider a population evolving under mutation and selection. The genotype of an individual is a word of length $\ell$ over a finite alphabet. Mutations occur during reproduction, independently on each locus; the fitness depends on the…
Consider a graph where the sites are distributed in space according to a Poisson point process on $\mathbb R^n$. We study a population evolving on this network, with individuals jumping between sites with a rate which decreases…