Hitting Probabilities: Markov Chains

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Explores the lower bound on total variation distance in Markov chains and its implications on mixing time.

Covers the basic theory for continuous time Markov chains and discusses communication, hitting probabilities, recurrence, and transience.

Explores recurrence, transience, and invariant distributions in Markov chains with proofs and examples.

Covers Markov chains, coupled chains, and their applications, emphasizing the importance of irreducibility.

Explores hitting probabilities in Markov chains, covering minimal solutions, proofs, and recursive relationships.

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Covers the approximation of functions in Sobolev spaces using smooth functions.

Explores sub/super harmonic functions and their applications in a theoretical context.

Explores the coupling of Markov chains and the proof of the ergodic theorem, emphasizing distribution convergence and chain properties.

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.