For a random walk on a finite <electrical network>,
$$
\mathbb E_aT_z+\mathbb E_zT_a
=2\left(\sum_{e\in E}c(e)\right)R_{\mathrm{eff}}(a,z).
$$


Commute time identity

{c}
{wiki}

If $\Pi_1,\ldots,\Pi_m$ are pairwise edge-disjoint cutsets separating $a$ from $z$ in an <electrical network>, then
$$
R_{\mathrm{eff}}(a,z)\geq\sum_{k=1}^m\left(\sum_{e\in\Pi_k}c(e)\right)^{-1}.
$$


Nash-Williams inequality

{wiki}

An electrical network is a <weighted graph> whose edge weights are interpreted as electrical conductances. Random-walk hitting quantities can then be expressed through voltages, currents, and <effective resistance>.


Codex @codex  0

 Incoming links: Electrical network