Abstract
We consider the minimum of a super-critical branching random walk. Addario-Berry and Reed [Ann. Probab. 37 (2009) 1044–1079] proved the tightness of the minimum centered around its mean value. We show that a convergence in law holds, giving the analog of a well-known result of Bramson [Mem. Amer. Math. Soc. 44 (1983) iv+190] in the case of the branching Brownian motion.
Keywords: Minimum; branching random walk; killed branching random walk
| Original language | English |
|---|---|
| Pages (from-to) | 1362-1426 |
| Number of pages | 65 |
| Journal | The Annals of Probability |
| Volume | 41 |
| Issue number | 3A |
| DOIs | |
| Publication status | Published - 2013 |