The TASEP on Galton–Watson trees

Nina Gantert, Nicos Georgiou, Dominik Schmid

Research output: Contribution to journalArticlepeer-review

Abstract

We study the totally asymmetric simple exclusion process (TASEP) on trees where particles are generated at the root. Particles can only jump away from the root, and they jump from x to y at rate rx,y provided y is empty. Starting from the all empty initial condition, we show that the distribution of the configuration at time t converges to an equilibrium. We study the current and give conditions on the transition rates such that the current is of linear order or such that there is zero current, i.e. the particles block each other. A key step, which is of independent interest, is to bound the first generation at which the particle trajectories of the first n particles decouple.

Original languageEnglish
Article number159
JournalElectronic Journal of Probability
Volume26
DOIs
StatePublished - 2021

Keywords

  • Current
  • Disentanglement
  • Exclusion process
  • Invariant measure
  • Totally asymmetric simple exclusion process
  • Trees

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