Random attraction in the TASEP model

Lars Gruene, Thomas Kriecherbauer, Michael Margaliot

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)65-93
Number of pages29
JournalSIAM Journal on Applied Dynamical Systems
Issue number1
StatePublished - 2021


  • Contraction
  • Random attractor
  • Random dynamical system
  • Ribosome flow model
  • Synchronization

All Science Journal Classification (ASJC) codes

  • Analysis
  • Modelling and Simulation


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