Related papers: Non-binary branching process and Non-Markovian exp…
For the critical Galton--Watson process with geometric offspring distributions we provide sharp barrier estimates for barriers which are (small) perturbations of linear barriers. These are useful in analyzing the cover time of finite graphs…
Branching Processes in a Random Environment (BPREs) $(Z_n:n\geq0)$ are a generalization of Galton Watson processes where in each generation the reproduction law is picked randomly in an i.i.d. manner. We determine here the upper large…
We study a nonlinear branching diffusion process in the sense of McKean, i.e., where particles are subjected to a mean-field interaction. We consider first a strong formulation of the problem and we provide an existence and uniqueness…
In this paper, we study the Galton-Watson process in the random environment for the particular case when the number of the offsprings in each generation has the fractional linear generation function with random parameters. In this case, the…
This article is an essay, both expository and argumentative, on the Galton-Watson process as a tool in the domain of Branching Processes. It is at the same time the author's ways to honour two distinguished scientists in this domain, both…
We study two types of stochastic processes, a mean-field spatial system of interacting Fisher-Wright diffusions with an inferior and an advantageous type with rare mutation (inferior to advantageous) and a (mean-field) spatial system of…
Looptrees have recently arisen in the study of critical percolation on the uniform infinite planar triangulation. Here we consider random infinite looptrees defined as the local limit of the looptree associated with a critical…
In this paper, we consider a critical Galton-Watson branching process with immigration stopped at zero $\mathbf{W}$. Some precise estimation on the generation function of the $n$-th population are obtained, and the tail probability of the…
Conditions for almost sure extinction are studied in discrete time branching processes with an infinite number of types. It is not assumed that the expected number of children is a bounded function of the parent's type. There might also be…
The Galton-Watson process is a model for population growth which assumes that individuals reproduce independently according to the same offspring distribution. Inference usually focuses on the offspring average as it allows to classify the…
In this article, we study concave recursions on trees, which appear widely in information theory through algorithms such as belief propagation, and in statistical mechanics through models on tree-like graphs, including the Ising model,…
Cheek and Johnston (Journal of Mathematical Biology, 2023) consider a continuous-time Bienaym\'e-Galton-Watson tree conditioned on being alive at time $T$. They study the reproduction events along the ancestral lineage of an individual…
Consider any supercritical Galton-Watson process which may become extinct with positive probability. It is a well-understood and intuitively obvious phenomenon that, on the survival set, the process may be pathwise decomposed into a…
We study biased random walk on subcritical and supercritical Galton-Watson trees conditioned to survive in the transient, sub-ballistic regime. By considering offspring laws with infinite variance, we extend previously known results for the…
A branching process in a Markovian environment consists of an irreducible Markov chain on a set of "environments" together with an offspring distribution for each environment. At each time step the chain transitions to a new random…
We study an extension of the so-called defective Galton-Watson processes obtained by allowing the offspring distribution to change over the generations. Thus, in these processes, the individuals reproduce independently of the others and in…
We consider a birth and death process in which death is due to both `natural death' and to competition between individuals, modelled as a quadratic function of population size. The resulting `logistic branching process' has been proposed as…
We study the iterated Galton-Watson process (IGW), possibly with thinning, introduced by Gawe{\l}and Kimmel to model the number of repeats of DNA triplets during some genetic disorders. If the process involves some thinning, then extinction…
We consider a branching random walk (BRW) taking its values in the $\mathtt{b}$-ary rooted tree $\mathbb W_{ \mathtt{b}}$ (i.e. the set of finite words written in the alphabet $\{ 1, \ldots, \mathtt{b} \}$, with $\mathtt{b}\! \geq \! 2$).…
We discuss complementary recurrence and transience criteria for stochastic processes $(X_n)_{n \ge 0}$ with values in the $d$-dimensional orthant $\mathbb R^d_+$ fulfilling a non-linear stochastic equation of the form $X_{n+1}=MX_n+g(X_n)+…