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 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.
Funding Statement
N. Georgiou acknowledges partial support from EPSRC First Grant EP/P021409/1: “The flat edge in last passage percolation” for the initial development of this project and by “The Dr Perry James (Jim) Browne Research Centre on Mathematics and its Applications” individual grant. D. Schmid thanks the Studienstiftung des deutschen Volkes and the TopMath program for financial support.
Acknowledgments
The research was partly carried out during visits of N. Gantert and D. Schmid to the University of Sussex and during visits of N. Georgiou to the Technical University of Munich. Grateful acknowledgement is made for hospitality to both universities. N. Georgiou and D. Schmid thank the Mathematisches Forschungsinstitut Oberwolfach for hospitality and support in the final stages of the project. Finally, we thank the anonymous referees and associate editor for their comments.
Citation
Nina Gantert. Nicos Georgiou. Dominik Schmid. "The TASEP on Galton–Watson trees." Electron. J. Probab. 26 1 - 38, 2021. https://doi.org/10.1214/21-EJP725
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