# Branching random walk in Z^4 with branching at the origin only - Mathematics > Probability

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Abstract: For the critical branching random walk in $\mathbb{Z}^{4}$ with branching atthe origin only we find the asymptotic behavior of the probability of the eventthat there are particles at the origin at moment $t ightarrow \infty $ andprove a Yaglom type conditional limit theorem for the number of individuals atthe origin given that there are particles at the origin.

Author: ** Yueyun Hu LAGA, Vladimir Vatutin, Valentin Topchii**

Source: https://arxiv.org/