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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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