One-point localization for branching random walk in Pareto environment

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

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...

Tail estimates for one-dimensional random walk in random environment

Suppose that the integers are assigned i.i.d. random variables f! x g (taking values in the unit interval), which serve as an environment. This environment deenes a random walk fX k g (called a RWRE) which, when at x, moves one step to the right with probability ! x , and one step to the left with probability 1 ? ! x. Solomon (1975) determined the almost-sure asymptotic speed (=rate of escape) ...

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...