Subsequential tightness for branching random walk in random 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.

Tightness for the Minimal Displacement of Branching Random Walk

Recursion equations have been used to establish weak laws of large numbers for the minimal displacement of branching random walk in one dimension. Here, we use these equations to establish the tightness of the corresponding sequences after appropriate centering. These equations are special cases of recursion equations that arise naturally in the study of random variables on tree-like structures...

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...

Branching random walk in Z with branching

For the critical branching random walk in Z 4 with branching at the origin only we find the asymptotic behavior of the probability of the event that there are particles at the origin at moment t → ∞ and prove a Yaglom type conditional limit theorem for the number of individuals at the origin given that there are particles at the origin.