Lectures related to Continuous-Time Markov Chains: Reversible Chains

Continuous-Time Markov Chains: Reversible Chains

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

Markov Chains: Ergodic Chains Examples

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

Continuous-Time Markov Chains: Reversible Chains

Covers reversible continuous-time Markov chains and their properties.

Markov Chains: Ergodic Chains Examples

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.

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 and Algorithm Applications

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

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.

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.

Ergodic Theorem: Proof and Applications

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

Limiting Distribution and Ergodic Theorem

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

Markov Chains: Reversibility & Convergence

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

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.

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: Convergence and Spectral Gap

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

Monte Carlo Moves in Simulation

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

Introduction to Quantum Chaos

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

Markov Chains: Properties and Approximations

Explores Markov chains' properties, hitting time, and Stirling's formula approximation.