Tightness for Maxima of Generalized Branching Random Walks

Details Tightness for Maxima of Generalized Branching Random Walks Tightness for Maxima of Generalized Branching Random Walks

2010-12-03

arxiv.org/abs/1012.0826v1

Mathematics

Probability

18 pages, no figure

Scientific paper

We study generalized branching random walks, which allow time dependence and local dependence between siblings. Under appropriate tail assumptions, we prove the tightness of $F_n(\cdot-Med(F_n))$, where $F_n(\cdot)$ is the maxima distribution at time $n$ and $Med(F_n)$ is the median of $F_n(\cdot)$. The main component in the argument is a proof of exponential decay of the right tail $1-F_n(\cdot-Med(F_n))$.

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