Continuous multi-line queues and TASEP

  • Erik Aas

    KTH - Royal Institute of Technology, Stockholm, Sweden
  • Svante Linusson

    KTH - Royal Institute of Technology, Stockholm, Sweden


In this paper, we study a distribution of labeled particles on a continuous ring. It arises in three different ways, all related to the multi-type TASEP on a ring. We prove formulas for the probability density function for some permutations and give conjectures for a larger class. We give a complete conjecture for the probability of two particles being next to each other on the cycle, for which we prove some cases. We also find that two natural events associated to the process have exactly the same probability expressed as a Vandermonde determinant. It is unclear whether this is just a coincidence or a consequence of a deeper connection.

Cite this article

Erik Aas, Svante Linusson, Continuous multi-line queues and TASEP. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 5 (2018), no. 1, pp. 127–152

DOI 10.4171/AIHPD/50