Related papers: Decomposable branching processes having a fixed ex…

We study the asymptotic behavior of the probability of non extinction of a weakly subcritical multitype branching process in iid random environments. Under suitable assumptions, the survival probability is of order of $\rho^n n ^{-3/2}$ for…

Consider a population whose size changes stepwise by its members reproducing or dying (disappearing), but is otherwise quite general. Denote the initial (non-random) size by $Z_0$ and the size of the $n$th change by $C_n$, $n= 1, 2,…

We consider the extinction time of the contact process on increasing sequences of finite graphs obtained from a variety of random graph models. Under the assumption that the infection rate is above the critical value for the process on the…

By introducing the notions of living and dead nodes a new model of random tree evolution with continuous time parameter has been constructed. It is assumed that two random variables, the lifetime and the offspring number of living nodes…

Consider $N$ particles performing random walks on the $\epsilon$-grid $(\epsilon Z)^d$, $\epsilon>0$ with branching and density-dependent selection: When one of the particles branches, a particle is removed from the most populated site. The…

We consider critical branching Brownian motion with absorption, in which there is initially a single particle at $x > 0$, particles move according to independent one-dimensional Brownian motions with the critical drift of $-\sqrt{2}$, and…

The asymptotic behavior of a stochastic network represented by a birth and death processes of particles on a compact state space is analyzed. Births: Particles are created at rate $\lambda_+$ and their location is independent of the current…

This paper gives conditions for the rightmost particle in the $n$th generation of a multitype branching random walk to have a speed, in the sense that its location divided by n converges to a constant as n goes to infinity. Furthermore, a…

We consider the long-time behaviour of a branching random walk in random environment on the lattice $\Z^d$. The migration of particles proceeds according to simple random walk in continuous time, while the medium is given as a random…

Consider a branching process $\{Z_n\}$ in a varying environment. Let $\{W_n\}$ be the natural martingale $Z_n/{\bf E}Z_n$. It converges to some random variable $W$ as $n\to\infty$. An important problem is to show that ${\bf P}(W>0)$ equals…

In the critical beta-splitting model of a random $n$-leaf rooted tree, clades are recursively split into sub-clades, and a clade of $m$ leaves is split into sub-clades containing $i$ and $m-i$ leaves with probabilities $\propto 1/(i(m-i))$.…

For a class of random partitions of an infinite set a de Finetti-type representation is derived, and in one special case a central limit theorem for the number of blocks is shown.

This paper is concerned with the characterizations of fixed points of the generating function of branching processes with countably infinitely many types. We assume each particle of type $i$ can only give offspring of type $j\geq i$, whose…

We consider an interacting particle system where equal-sized populations of two types of particles move by random walk steps on a graph, the two types may have different speeds, and meetings of opposite-type particles result in…

We finely describe the "coming down from infinity" for birth and death processes which eventually become extinct. Our biological motivation is to study the decrease of regulated populations which are initially large. Under general…

We study the critical centered branching random walk with offspring and displacement distributions having finite variance, under minimal assumptions on its structure. We show that the probability that the position of the right-most particle…

The fitness of a biological strategy is typically measured by its expected reproductive rate, the first moment of its offspring distribution. However, strategies with high expected rates can also have high probabilities of extinction. A…

Let $(Z_n)_{n\geqslant 0}$ be a branching process in a random environment defined by a Markov chain $(X_n)_{n\geqslant 0}$ with values in a finite state space $\mathbb X$ starting at $X_0=i \in\mathbb X$. We extend from the i.i.d.…

Recently, neuronal avalanches have been observed to display oscillations, a phenomenon regarded as the co-existence of a scale-free behaviour (the avalanches close to criticality) and scale-dependent dynamics (the oscillations). Ordinary…

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…