Stationary Distribution Markov Chain Interview Guide
Stationary distribution Markov chain interview guide for long-run probabilities, balance equations, conditions, examples, and caveats.
Candidates solving long-run state probability questions.
A stationary distribution is unchanged by transition
A stationary distribution is a probability vector that remains the same after applying the transition matrix. It represents a distribution-level equilibrium, not necessarily a starting state.
Solve balance plus normalization
For small chains, solve the stationarity equation along with probabilities summing to one. Keep matrix orientation consistent with the transition convention.
Concrete example
In a two-state chain, the long-run share in each state can often be found by balancing flow from A to B with flow from B to A, then normalizing.
Conditions matter
Not every chain has a unique useful limiting distribution from every start. Reducibility, periodicity, and absorbing states can change the interpretation.
Common mistakes
Candidates often assume stationary means the chain never moves. It means the distribution over states is stable, even though individual paths keep transitioning.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.