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An upper bound for the probability of visiting a distant point by a critical branching random walk in $$\mathbb{Z} ^{4}$$. (English) Zbl 07068656
Summary: In this paper, we study the probability of visiting a distant point $$a\in \mathbb{Z} ^{4}$$ by a critical branching random walk starting at the origin. We prove that this probability is bounded by $$1/backslash(|a|^{2}\log |a|)$$ up to a constant factor.

##### MSC:
 60G50 Sums of independent random variables; random walks 60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
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##### References:
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