Lectures related to Markov Chains: Reversibility & Convergence

Geometric Ergodicity: Convergence Diagnostics

Covers the concept of geometric ergodicity in the context of convergence diagnostics for Markov chains.

Coupling of Markov Chains: Ergodic Theorem

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

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 Chain Monte Carlo

Covers the Markov Chain Monte Carlo method and the Metropolis-Hastings algorithm for generating samples from a target probability distribution.

Markov Chains: Theory and Applications

Covers the theory and applications of Markov chains, focusing on key concepts and properties.

Markov Chains: Ergodicity and Stationary Distribution

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

Markov Chains: Ergodic Chains Examples

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

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.

Continuous-Time Markov Chains: Reversible Chains

Covers reversible continuous-time Markov chains and their properties.

Markov Chains: PageRank Algorithm

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

Estimating Relaxation Time: Variance and Chains

Covers the estimation of relaxation time in chains and the importance of sample sizes.

Markov Chains: Ergodic Chains Examples

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

Lower Bound on Total Variation Distance

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

Introduction to Quantum Chaos

Covers the introduction to Quantum Chaos, classical chaos, sensitivity to initial conditions, ergodicity, and Lyapunov exponents.

Markov Chains: Reversibility and Stationary Distribution

Explores reversibility in Markov chains and its impact on the stationary distribution, highlighting the complexity of non-reversible chains.

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.

Joint Equidistribution of CM Points

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

Stochastic Simulation: Markov Chains and Metropolis Hastings

Introduces Markov chains and Metropolis Hastings algorithm in stochastic simulation.

Stochastic Processes: Time Reversal

Explores time reversal in stationary Markov chains and the concept of detailed balance conditions.