Lectures related to Coupling of Markov Chains: Ergodic Theorem

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

Explores the proof of the ergodic theorem using total variation distance and coupling concepts.

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Explores Markov chains and their applications in algorithms, focusing on user impatience and faithful sample generation.

Correlations of the Liouville function

Explores correlations of the Liouville function along deterministic and independent sequences, covering key concepts and theorems.

Lower Bound on Total Variation Distance

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

Markov Chains: Reversibility & Convergence

Covers Markov chains, focusing on reversibility, convergence, ergodicity, and applications.

Markov Chains: Ergodic Chains Examples

Covers stochastic models for communications, focusing on discrete-time Markov chains.

Joint Equidistribution of CM Points

Covers the joint equidistribution of CM points and the ergodic decomposition theorem in compact abelian groups.

Markov Chains: Ergodic Chains Examples

Covers stochastic models for communications, focusing on discrete-time Markov chains.

Limiting Distribution and Ergodic Theorem

Explores limiting distribution in Markov chains and the implications of ergodicity and aperiodicity on stationary distributions.

A Conjecture of Erdös: Proof by Moreira, Richter and Robertson

Presents a short proof of a conjecture by Erdös, exploring related questions and detailed proof of the proposition.

Markov Chains Decomposition

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

Markov Chains: Ergodicity and Stationary Distribution

Explores ergodicity and stationary distribution in Markov chains, emphasizing convergence properties and unique distributions.

Theory of MCMC

Covers the theory of Markov Chain Monte Carlo (MCMC) sampling and discusses convergence conditions, transition matrix choice, and target distribution evolution.

Markov Chains: Applications and Coupled Chains

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

Stochastic Simulation: Theory of Markov Chains

Covers the theory of Markov chains, focusing on reversible chains and detailed balance.

Markov Chains and Algorithm Applications

Covers Markov chains and their applications in algorithms, focusing on Markov Chain Monte Carlo sampling and the Metropolis-Hastings algorithm.

Convergence in Law: Theorem and Proof

Explores convergence in law for random variables, including Kolmogorov's theorem and proofs based on probability lemmas.

Markov Chains: PageRank Algorithm

Explores the PageRank algorithm within Markov chains, emphasizing ergodicity and convergence for web page ranking.