Abstract
We consider a branching random walk on $R$ with a killing barrier at zero. At criticality, the process becomes eventually extinct, and the total progeny $Z$ is therefore finite. We show that $P(Z>n)$ is of order $(nln2(n))-1$, which confirms the prediction of Addario-Berry and Broutin [1].
| Original language | English |
|---|---|
| Pages (from-to) | 522-533 |
| Journal | Electronic Communications in Probability |
| Volume | 15 |
| Publication status | Published - 2010 |