Let $G$ be the (random) graph which is the union of two independent copies of the uniform spanning forest on $\mathbb{Z}^3$.
Question: Is (the simple random walk on) $G$ transient almost surely?
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1$\begingroup$ I'm confused. Are you sure your question is complete? What are you asking to show is transient? Usually that refers to a random walk, right? How is that related to the spanning forests? $\endgroup$– Sam HopkinsCommented Mar 25, 2023 at 23:13
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$\begingroup$ @SamHopkins There is a strictly definition that transient random graph. But in this question, the random walk is just the simple random walk. $\endgroup$– none YuanCommented Mar 26, 2023 at 20:08
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