Friedlin Wentzell solutions of discrete Hamilton Jacobi equations
The Markov chain tree theorem gives a combinatorial representation of the unique invariant measure for irreducible Markov chains, expressible in the form of weights on geometric structures called rooted arborescences. By considering the thermodynamic limit of the detailed balance condition satisfied by the measure, we obtain a discrete equation (Hamilton-Jacobi equation) of which we are able to classify all the solutions, and one of them (Freidlin-Wentzell solution) derives directly from the combinatorial representation of the measure itself.
Area: CS52 - Trees and combinatorial probability (Michele Aleandri)
Keywords: Trees, Arborescences, Markov Chains, Exclusion Process
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