Branching random walk in Z^4 with branching at the origin only

Abstract

For the critical branching random walk in ${\mathbb{Z}}^4$ 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 $t\to \infty$ and prove a Yaglom type conditional limit theorem for the number of individuals at the origin given that there are particles at the origin.