Lectures related to Markov Chains: PageRank Algorithm

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

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.

Limiting Distribution and Ergodic Theorem

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

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 Chains: Ergodic Chains Examples

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

Ergodic Theorem: Proof and Applications

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

Ergodic Theory: Markov Chains

Explores ergodic theory in Markov chains, discussing irreducibility and unique stationary distributions.

Markov Chains: Reversibility & Convergence

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

Lower Bound on Total Variation Distance

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

Continuous-Time Markov Chains: Reversible Chains

Covers reversible continuous-time Markov chains and their properties.

Continuous-Time Markov Chains: Reversible Chains

Covers Mod.7 on continuous-time Markov chains, focusing on reversible chains and their applications in communication systems.

Continuous-Time Markov Chains: Reversible Chains

Covers continuous-time Markov chains, focusing on reversible chains and their properties.

Markov Chains: Convergence and Spectral Gap

Explores Markov chain convergence, spectral gap, and acceleration techniques for faster convergence.

Invariant Measures: Properties and Applications

Covers the concept of invariant measures in Markov chains and their role in analyzing irreducible recurrent processes.

Asymptotic Behavior of Markov Chains

Explores recurrent states, invariant distributions, convergence to equilibrium, and PageRank algorithm.

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: Homogeneous Processes and Stationary Distributions

Explores Markov chains, focusing on homogeneous processes and stationary distributions, with practical exercises.