Lectures related to Page Rank: Theory and Convergence

Markov Chains: PageRank Algorithm

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

Pseudorandomness: Theory and Applications

Explores pseudorandomness theory, AI challenges, pseudo-random graphs, random walks, and matrix properties.

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.

Markov Chains: Ergodic Chains Examples

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

Invariant Distributions: Markov Chains

Explores invariant distributions, recurrent states, and convergence in Markov chains, including practical applications like PageRank in Google.

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: Ergodicity and Stationary Distribution

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

Asymptotic Behavior of Markov Chains

Explores recurrent states, invariant distributions, convergence to equilibrium, and PageRank 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: Homogeneous Processes and Stationary Distributions

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

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 and Algorithm Applications

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

Ergodic Theorem: Proof and Applications

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

Markov Chains: Applications and Sampling Methods

Covers the basics of Markov chains and their algorithmic applications.

Spectral Gap in Markov Chains

Explores the spectral gap in Markov chains and its impact on convergence speed.

Limiting Distribution and Ergodic Theorem

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

Invariant Measures: Properties and Applications

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

Ergodic Theory: Markov Chains

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

Bonus Malus System: Transition Probabilities

Explores the Bonus Malus system for insurance premiums and Markov chain transition probabilities.