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arxiv: 2304.08225 · v2 · pith:XMTPIFATnew · submitted 2023-04-17 · 🧮 math.PR

Percolation threshold for metric graph loop soup

classification 🧮 math.PR
keywords metricgraphgraphslooppercolationsoupthresholdclass
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In this short note, we show that the critical threshold for the percolation of metric graph loop soup on a large class of transient metric graphs (including quasi-transitive graphs such as $\mathbb{Z}^d$, $d\geq 3$) is $1/2$.

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