On the critical branching random walk I: Branching capacity and visiting probability

2016/11/30 by Zhu, Qingsan · 2 citations
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1611.10324

Abstract

We extend the theory of discrete capacity to critical branching random walk. We introduce branching capacity for any finite subset of \Z^d, d≥5. Analogous to the regular discrete capacity, branching capacity is closely related to the asymptotics of the probability of visiting a fixed finite set by a critical branching random walk starting from a distant point and the conditional distribution of the hitting point.

Cited by

• Derivative formula for capacities
• Capacity in high dimensional percolation

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