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Random attraction in the TASEP model

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. 65-93.
ISSN 1536-0040
DOI: https://doi.org/10.1137/20M131446X

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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 almost surely. 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: Article in a journal
Refereed: Yes
Keywords: Ribosome flow model; contraction; random dynamical systems; random attractor; synchronization; mRNA translation
Subject classification: MSC subject classification: 37H99, 34D06, 37A60
Mathematics Subject Classification Code: 60K35 (34D06 37H05 37L55 82C20)
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: 12 Jan 2021 08:00
Last Modified: 18 Mar 2021 12:50
URI: https://eref.uni-bayreuth.de/id/eprint/61566

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