Topic: Convergence to Equilibrium and Ergodic Theorems

Lower Bounds from Slow Escape and Bottleneck Sets

Long-Run Averages of State Rewards

Lazification and Aperiodic Chain Construction

Finite-State Convergence by a Positive Transition Power

Exact Mixing-Time Calculations for Two-State Chains

Ergodic Limits in Chains with Multiple Closed Classes

Empirical Frequencies of States

Doeblin Minorization and Geometric Contraction

Distinguishing Distributional Convergence from Time Averages

Couplings and the Coupling Inequality