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We consider a branching random walk on the lattice, where the branching rates are given by an i.i.d. Pareto random potential. We show that the system of particles, rescaled in an appropriate way, converges in distribution to a scaling limit that is interesting in its own right. We describe the limit object as a growing collection of lilypads built on a Poisson point process in $mathbb{R}^d$. As an application of our main theorem, we show that the maximizer of the system displays the ageing property.
Using a high performance computer cluster, we run simulations regarding an open problem about d-dimensional critical branching random walks in a random IID environment The environment is given by the rule that at every site independently, with probab
We consider branching random walks in $d$-dimensional integer lattice with time-space i.i.d. offspring distributions. When $d ge 3$ and the fluctuation of the environment is well moderated by the random walk, we prove a central limit theorem for the
We consider the branching process in random environment ${Z_n}_{ngeq 0}$, which is a~population growth process where individuals reproduce independently of each other with the reproduction law randomly picked at each generation. We focus on the super
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 structure. F
In this article, we consider a Branching Random Walk (BRW) on the real line where the underlying genealogical structure is given through a supercritical branching process in i.i.d. environment and satisfies Kesten-Stigum condition. The displacements