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The Minimal Position of a Stable Branching Random Walk
Jingning Liu, Mei Zhang · 2017-12-25 · via math.PR updates on arXiv.org

In this paper, a branching random walk $(V(x))$ in the boundary case is studied, where the associated one dimensional random walk is in the domain of attraction of an $α-$stable law with $1<α<2$. Let $M_n$ be the minimal position of $(V(x))$ at generation $n$. We established an integral test to describe the lower limit of $M_n-\frac{1}α\log n$ and a law of iterated logarithm for the upper limit of $M_n-(1+\frac{1}α)\log n$.

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