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THE FIVE GREATEST APPLICATIONSOFMARKOV CHAINSPHILIPP VON HILGERS ANDAMY N. LANGVILLE hundred years removed from A. A. markov s development ofhis chains, we takestock of the field he generated and the mathematical impression he left. As a tribute to markov , wepresent what we consider to be the five greatest applicationsof markov chains, markov applications, stationary vector, PageRank, HIdden Markovmodels, performance evaluation, Eugene Onegin, information theoryAMS subject , 60J20, 60J22, 60J27, 65C401. five applications that we have selected are presented inthe boring but traditional chronological order. Of course,we agree that this orderingscheme is a bit unfair and problematic.

Markov chains in the new domain of communication systems, processing “symbol by symbol” [30] as Markov was the first to do. However, Shannon went beyond Markov’s work with his information theory application. Shannon used Markov chains not solely

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