Diameters of Symmetric and Lifted Simple Exclusion Models

We determine diameters of Markov chains describing one-dimensional N -particle models with an exclusion interaction, namely the symmetric simple exclusion process ( Ssep ) and one of its non-reversible liftings, the lifted totally asymmetric simple exclusion process ( Tasep ). The diameters provide lower bounds for the mixing times, and we discuss the implications of our findings for the analysis of these models.