Equilibrium measure of a finite set ( $e_{A}$ )

The equilibrium measure is supported on

A

and is given by

e_{A} (x) = 1_{{x \in A}} μ_{x} P_{x} (H_{A} = \infty) .

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- Capacity of a finite set for a transient random walk Equilibrium measure of a finite set

Capacity of a finite set for a transient random walk ( $cap (A)$ )

The capacity of a finite set is the total mass of its equilibrium measure of a finite set:

cap (A) = \sum_{x} e_{A} (x) = E (h_{A}, h_{A}) .

Capacity is monotone under inclusion, though strict inclusion need not give strict inequality.

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