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arXiv · 1012.0826

Tightness for Maxima of Generalized Branching Random Walks

Ming Fang
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Abstract

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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Ming Fang. 2010-12-03. Tightness for Maxima of Generalized Branching Random Walks. https://arxiv.org/abs/1012.0826

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