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Distance and resistance on random series-parallel graphs: logarithmic speeds and near-critical asymptotics
We study the graph distance $D_n(p)$ and effective resistance $R_n(p)$ between the boundary vertices of a depth-$n$ random series--parallel graph, obtained by recursively joining two independent copies in series with probability $p$ and in parallel with probability $1-p$. We prove the existence of d
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