Steady-state random walk on connected graph of arbitrary topology with random and non-symmetric transition rates

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Abstract

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The general solution and its graphical interpretation for the stationary occupation probability of nodes for a random-walk on a connected network of arbitrary topology with random and non-symmetric transition rates are presented. Configurational averaging over the quenched random transition rates is performed for several simple networks: open chains, simple and general stars, two interacting stars. It is demonstrated that disorder in transition rates for a random walker induces variable occupation probability for different nodes in the network depending on their location. The boundary nodes are shown to be occupied with higher probability than the central ones.

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