Related papers: Persistence of competing systems of branching rand…
We consider a sequence of Poisson cluster point processes on $\mathbb{R}^d$: at step $n\in\mathbb{N}_0$ of the construction, the cluster centers have intensity $c/(n+1)$ for some $c>0$, and each cluster consists of the particles of a…
Local perturbations in conservative particle systems can have a non-local influence on the stationary measure. To capture this phenomenon, we analyze in this paper two toy models. We study the symmetric exclusion process on a countable set…
We consider the simple random walk on random graphs generated by discrete point processes. This random graph has a random subset of a cubic lattice as the vertices and lines between any consecutive vertices on lines parallel to each…
We consider a continuous-time branching random walk on $\mathbb{Z}$ in a random non homogeneous environment. Particles can walk on the lattice points or disappear with random intensities. The process starts with one particle at initial time…
In this paper we prove that, under the assumption of quasi-transitivity, if a branching random walk on ${{\mathbb{Z}}^d}$ survives locally (at arbitrarily large times there are individuals alive at the origin), then so does the same process…
We consider simple random walks on Delaunay triangulations generated by point processes in $\mathbb{R}^d$. Under suitable assumptions on the point processes, we show that the random walk satisfies an almost sure (or quenched) invariance…
We consider a time-continuous branching random walk on a one-dimensional lattice on which there is one center (lattice point) of particle generation, called branching source. The generation of particles in the branching source is described…
By decomposing the random walk path, we construct a multitype branching process with immigration in random environment for corresponding random walk with bounded jumps in random environment. Then we give two applications of the branching…
We consider a branching random walk in a random space-time environment of disasters where each particle is killed when meeting a disaster. This extends the model of the "random walk in a disastrous random environment" introduced by [15]. We…
We are interested in the survival probability of a population modeled by a critical branching process in an i.i.d. random environment. We assume that the random walk associated with the branching process is oscillating and satisfies a…
In this paper, we introduce a one-dimensional model of particles performing independent random walks, where only pairs of particles can produce offspring ("cooperative branching"), and particles that land on an occupied site merge with the…
Let $\left\{ Z_{n},n=0,1,2,...\right\} $ be a critical branching process in random environment and let $\left\{ S_{n},n=0,1,2,...\right\} $ be its associated random walk. It is known that if the increments of this random walk belong…
We consider a branching-selection particle system on the real line, introduced by Brunet and Derrida. In this model the size of the population is fixed to a constant $N$. At each step individuals in the population reproduce independently,…
The continuous-time random walk is defined as a Poissonization of discrete-time random walk. We study the noncolliding system of continuous-time simple and symmetric random walks on ${\mathbb{Z}}$. We show that the system is determinantal…
The persistence probability, $P_C(t)$, of a cluster to remain unaggregated is studied in cluster-cluster aggregation, when the diffusion coefficient of a cluster depends on its size $s$ as $D(s) \sim s^\gamma$. In the mean-field the problem…
We study branching processes in an i.i.d. random environment, where the associated random walk is of the oscillating type. This class of processes generalizes the classical notion of criticality. The main properties of such branching…
The notion of stability can be generalised to point processes by defining the scaling operation in a randomised way: scaling a configuration by $t$ corresponds to letting such a configuration evolve according to a Markov branching particle…
We investigate a branching random walk where the displacements are independent from the branching mechanism and have a stretched exponential distribution. We describe the positions of the particles in the vicinity of the rightmost particle…
We study a discrete-time branching annihilating random walk (BARW) on the $d$-dimensional lattice. Each particle produces a Poissonian number of offspring with mean $\mu$ which independently move to a uniformly chosen site within a fixed…
We study a continuous-time branching random walk on the lattice $\mathbb{Z}^{d}$, $d\in \mathbb{N}$, with a single source of branching, that is the lattice point where the birth and death of particles can occur. The random walk is assumed…