Lectures related to Markov Chains: Convergence and Spectral Gap

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.

Markov Chains: PageRank Algorithm

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

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.

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.

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.

Markov Chains: Reversibility & Convergence

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

Continuous-Time Markov Chains: Reversible Chains

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

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

Continuous-Time Markov Chains: Reversible Chains

Covers reversible continuous-time Markov chains and their properties.

Lower Bound on Total Variation Distance

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

Ergodic Theory: Markov Chains

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

Invariant Measures: Properties and Applications

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

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: Communicating Classes

Explores communicating classes in Markov chains, distinguishing between transient and recurrent classes, and delves into the properties of these classes.

Monte Carlo Moves in Simulation

Explores Monte Carlo moves in simulation, including trial moves and biased moves, comparing Monte Carlo with Molecular Dynamics.