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Random attraction in the TASEP model

Title data

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

Official URL: Volltext

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Project information

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 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.

Further data

Item Type: Preprint, postprint
Refereed: No
Keywords: Ribosome flow model; contraction; random dynamical systems; random attractor; synchronization; mRNA translation
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics VI (Nonlinear Analysis and Mathematical Physics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics VI (Nonlinear Analysis and Mathematical Physics) > Chair Mathematics VI (Nonlinear Analysis and Mathematical Physics) - Univ.-Prof. Dr. Thomas Kriecherbauer
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Research Institutions > Research Centres > Forschungszentrum für Modellbildung und Simulation (MODUS)
Research Institutions
Research Institutions > Research Centres
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
500 Science > 570 Life sciences, biology
Date Deposited: 27 Jan 2020 14:21
Last Modified: 27 Jan 2020 14:21
URI: https://eref.uni-bayreuth.de/id/eprint/54198