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- ItemCombinatorial considerations on the invariant measure of a stochastic matrix(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Stephan, ArturThe invariant measure is a fundamental object in the theory of Markov processes. In finite dimensions a Markov process is defined by transition rates of the corresponding stochastic matrix. The Markov tree theorem provides an explicit representation of the invariant measure of a stochastic matrix. In this note, we given a simple and purely combinatorial proof of the Markov tree theorem. In the symmetric case of detailed balance, the statement and the proof simplifies even more.