Annales de l’Institut Henri Poincaré D


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Volume 5, Issue 1, 2018, pp. 127–152
DOI: 10.4171/AIHPD/50

Published online: 2018-02-01

Continuous multi-line queues and TASEP

Erik Aas[1] and Svante Linusson[2]

(1) KTH - Royal Institute of Technology, Stockholm, Sweden
(2) KTH - Royal Institute of Technology, Stockholm, Sweden

In this paper, we study a distribution $\Xi$ 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 $i, j$ 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.

Keywords: TASEP, exclusion process, multiline queue

Aas Erik, Linusson Svante: Continuous multi-line queues and TASEP. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 5 (2018), 127-152. doi: 10.4171/AIHPD/50