3.0

credits

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This course explores modern approaches to Markov chains, with a focus on Markov chain mixing theory, which originated in the 1980s. Unlike classical methods that estimate the rate of convergence to stationarity as time increases to infinity, mixing time analysis concentrates on the number of steps required to reach a specified distance to the stationary distribution. Its study has various applications in fields such as computer science, statistical physics, and other areas of mathematics. The course will rigorously develop the underlying mathematics, covering essential techniques such as coupling, strong stationary times, spectral methods, and others. Key topics will also include random walks and electrical networks, cover times, cutoffs, and some analytical tools.