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We investigate the stationary distribution of asymmetric and weaklyasymmetric simple exclusion processes with open boundaries. We project thestationary distribution onto a subinterval, whose size is allowed to grow withthe length of the underlying segment. Depending on the boundary parameters ofthe exclusion process, we provide conditions such that the stationarydistribution projected onto a subinterval is close in total variation distanceto a product measure.

Approximating the stationary distribution of the ASEP with open boundaries