A minimal-trees-representation for the invariant measure of boundary driven exclusion processes
The Markov chain tree theorem gives a tree-representation for the invariant measure of Markov chains: we use it in the analysis of boundary driven exclusion processes. If we start from the one-dimensional case, by considering the large deviation limit, we can restrict the measure to minimal trees only. In this way we can easily compute the measure, obtaining a Bernoulli's distribution. This allows us to write an expression for the invariant measure for exclusion processes in higher dimensions, with multiple sources, and different geometrical structures. Finally, we generalize the result to continuous-time Markov chains.
Area: CS52 - Trees and combinatorial probability (Michele Aleandri)
Keywords: Trees, Arborescences, Markov Chains, Exclusion Process
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