Title data
Grüne, Lars ; Kriecherbauer, Thomas ; Margaliot, Michael:
Random attraction in the TASEP model.
In: SIAM Journal on Applied Dynamical Systems.
Vol. 20
(January 2021)
Issue 1
.
 pp. 6593.
ISSN 15360040
DOI: https://doi.org/10.1137/20M131446X
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Project financing: 
Israel Science Foundation Grants 

Abstract in another language
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 wellknown 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 almost surely. This implies that in the long run TASEP "filters out" any perturbation that changes the state of the particles along the chain.
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Random attraction in the TASEP model. (deposited 27 Jan 2020 14:21)
 Random attraction in the TASEP model. (deposited 12 Jan 2021 08:00) [Currently Displayed]