Lectures related to Hitting Probabilities: Markov Chains

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.

Explores the chain rule for compositions of differential functions in higher dimensions, emphasizing gradients and directional changes.

Explains the proof of the ergodic theorem and the concept of positive-recurrence in Markov chains.

Explores the theory of optimal transport, focusing on Lipschitz functions and uniqueness of solutions.

Covers the Meyers-Serrin theorem in analysis, discussing the conditions for functions in different spaces.

Explores the theorems on maximum and minimum values of functions and their relation to continuity.

Covers the generalization of the TAF theorem, lateral derivatives, limits of derivatives, and indeterminacy.

Covers Markov chains decomposition, LLN proof, Inventory Model application, and average costs.

Covers the definition of the center of a function using finite differences and provides step-by-step proofs.

Introduces Coq, covering defining propositions, proving theorems, and using tactics.

Explores modular arithmetic, emphasizing inverses and equations in Z/mZ, with practical examples and exercises.