Critical branching random walk in an IID environment

Critical branching random walk in an IID environment

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 probability p 2 Œ0; 1 , there is a cookie, completely suppressing the branching of any particle located there. The simulations suggest self averaging: t...

Central Limit Theorem in Multitype Branching Random Walk

A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.

Branching Random Walk in Random Environment: Fully Quenched Case

The critical branching random walk in a random environment dies out

We study the possibility for branching random walks in random environment (BRWRE) to survive. The particles perform simple symmetric random walks on the d-dimensional integer lattice, while at each time unit, they split into independent copies according to time-space i.i.d. offspring distributions. As noted by Comets and Yoshida, the BRWRE is naturally associated with the directed polymers in r...

Annealed Moment Lyapunov Exponents for a Branching Random Walk in a Homogeneous Random Branching Environment∗

We consider a continuous-time branching random walk on the lattice Z (d ≥ 1) evolving in a random branching environment. The motion of particles proceeds according to the law of a simple symmetric random walk. The branching medium formed of Markov birth-and-death processes at the lattice sites is assumed to be spatially homogeneous. We are concerned with the long-time behavior of the quenched m...