Continuous multiline queues and the TASEP on a ring

Abstract. I will discuss a distribution on finite number of labelled particles on a continuous ring. It arises in three different ways, all related to the multi-type TASEP on a ring. I will present several conjectures about properties of this distribution for which we can only prove some special cases. One such conjecture is for the probability density function and another is a conjecture for the probability of two particles i, j being next to each other on the cycle.