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Markovchains are often described by a directed graph, where the edges are labeled by the probabilities of going from one state to the other states.
Markovchains also have many applications in biological modelling, particularly population processes, which are useful in modelling processes that are (at least) analogous to biological populations.
Markovchains are related to Brownian motion and the ergodic hypothesis, two topics in physics which were important in the early years of the twentieth century, but Markov appears to have pursued this out of a mathematical motivation, namely the extension of the law of large numbers to dependent events.