The exclusion process is one of the best-studied examples of an interacting particle system. In this talk, we consider the stationary distribution of asymmetric simple exclusion processes with open boundaries. We project the stationary distribution onto a subinterval, whose size is allowed to grow with the length of the underlying segment. Depending on the boundary parameters for the exclusion process, we provide sufficient conditions such that the projected stationary distribution is close in total variation distance to a product measure. This talk is based on joint work with Evita Nestoridi.