On the critical branching random walk III: the critical dimension

Qingsan Zhu

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arXiv · 1701.08917

On the critical branching random walk III: the critical dimension

Qingsan Zhu

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Abstract

In this paper, we study the critical branching random walk in the critical dimension, $Z^4$. We provide the asymptotics of the probability of visiting a fixed finite subset and the range of the critical branching random walk conditioned on the total number of offsprings. We also prove that conditioned on visiting, the first visiting point converges in distribution.

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Qingsan Zhu. 2017-01-31. On the critical branching random walk III: the critical dimension. https://arxiv.org/abs/1701.08917

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