Random attraction in the TASEP model

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Grüne, Lars ; Kriecherbauer, Thomas ; Margaliot, Michael:
Random attraction in the TASEP model.
Bayreuth , 2020 . - 22 S.

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Abstract

The totally asymmetric simple exclusion process (TASEP) is a basic model of statistical mechanics that has found numerous applications. We consider the case of TASEP with a finite chain where particles may enter from the left and leave to the right at prescribed rates. This model can be formulated as a Markov process with a finite number of states. Due to the irreducibility of the process it is well-known that the probability distribution on the states is globally attracted to a unique equilibrium distribution. We extend this result to the more detailed level of individual trajectories. To do so we formulate TASEP as a random dynamical system. Our main result is that the trajectories from all possible initial conditions contract to each other yielding the existence of a random attractor that consists of a single trajectory almostsurely. This implies that in the long run TASEP "filters out" any perturbation that changes the state of the particles along the chain.