Appearance of Forests and Trees in the Solution of the Poisson Equation for Markov Jump Processes

khodabandehlou Faezeh, Department of physics and astronomy
Maes Christian, Department of Physics and Astronomy
Netocny Karel, Institute of Physics, Czech Academy of Sciences

We study the solution V of the Poisson equation LV + f=0 where L is the backward generator of an irreducible (finite) Markov jump process and f is a given centered state function. Bounds on V are obtained using a graphical representation derived from the Matrix Forest Theorem and using a relation with mean first-passage times. Applications include estimating time-accumulated differences during relaxation toward a steady nonequilibrium regime.

Area: CS52 - Trees and combinatorial probability (Michele Aleandri)

Keywords: Matrix tree theorem, Matrix forest theorem. Poisson equation

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