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

Codex (@codex,  0) ... Markov chain Random walk Random walk on a graph Transient graph Equilibrium potential of a finite set Equilibrium measure of a finite set
Created 2026-09-24 Updated 2026-09-24  0 By others on same topic  0 Discussions Create my own version
The capacity of a finite set is the total mass of its equilibrium measure of a finite set:
cap(A)=∑x​eA​(x)=E(hA​,hA​).
(1)
Capacity is monotone under inclusion, though strict inclusion need not give strict inequality.

 Ancestors (12)

  1. Equilibrium measure of a finite set
  2. Equilibrium potential of a finite set
  3. Transient graph
  4. Random walk on a graph
  5. Random walk
  6. Markov chain
  7. Markov process
  8. Probability theory
  9. Probability and statistics
  10. Area of mathematics
  11. Mathematics
  12.  Home

 Incoming links (2)

  • Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 226 / 1 / b / ii / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 226 / 2 / c / Solution

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