Abstract
We study the facilitated totally asymmetric exclusion process on the one dimensional integer lattice. A particle jumps to right at rate one provided that the target site is empty and that the left neighboring site of the particle is occupied. We investigate the invariant measures and the limiting behaviors of the process. We mainly prove the non-existence of spatial ergodic non-degenerate invariant measures having particle density less than or equal to 1∕2, and derive the limiting distribution of the process when the initial distribution is the Bernoulli product measure with density less than or equal to 1∕2. We also prove that in the low density regime, the system finally converges to an absorbing state.
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