\BOOKMARK [2][-]{subsection.0.1}{Application: Bigram and trigram models}{}% 1
\BOOKMARK [1][-]{section.1}{Recasting a random walk as linear algebra}{}% 2
\BOOKMARK [2][-]{subsection.1.1}{Mixing Time}{section.1}% 3
\BOOKMARK [1][-]{section.2}{Upper bounding the mixing time \(undirected d-regular graphs\)}{}% 4
\BOOKMARK [2][-]{subsection.2.1}{Application 2: Metropolis Algorithm and Multivariate Statistics }{section.2}% 5
\BOOKMARK [1][-]{section.3}{Analysis of Mixing Time for General Markov Chains}{}% 6