Markov Chains: Reversibility & Convergence

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

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

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

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

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

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

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

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

Introduces Markov chains and Metropolis Hastings algorithm in stochastic simulation.

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