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An exact solution of a one-dimensional asymmetric exclusion model with open boundaries. (English) Zbl 0893.60077
Summary: A simple asymmetric exclusion model with open boundaries is solved exactly in one dimension. The exact solution is obtained by deriving a recursion relation for the steady state: if the steady state is known for all system sizes less than $$N$$, then an equation gives the steady state for size $$N$$. Using this recursion, we obtain closed expressions for the average occupations of all sites. The results are compared to the predictions of a mean field theory. In particular, for infinitely large systems, the effect of the boundary decays as the distance to the power $$-1/2$$ instead of the inverse of the distance, as predicted by the mean field theory.

##### MSC:
 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82C22 Interacting particle systems in time-dependent statistical mechanics
##### Keywords:
asymmetric exclusion process; steady state; phase diagram
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