Continuous Multi-line Queues and TASEP
Abstract
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 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.
Cite
@article{arxiv.1501.04417,
title = {Continuous Multi-line Queues and TASEP},
author = {Erik Aas and Svante Linusson},
journal= {arXiv preprint arXiv:1501.04417},
year = {2017}
}
Comments
Accepted for publication in Annales de l'Institut Henri Poincare D, Combinatorics, Physics and their Interactions