Correlations in the continuous multispecies TASEP on a ring

In this paper, we prove a conjecture proposed by Aas and Linusson regarding the two-point correlations of adjacent particles in a continuous multispecies TASEP on a ring (AIHPD, 2018). We use the theory of multiline queues, as devised by Ferrari and Martin (AOP, 2008), to interpret the conjecture in terms of the placements of numbers in triangular arrays. Further, we use projections to calculate the correlations in the continuous multispecies TASEP using a distribution on these placements.