Correlations in the continuous multispecies TASEP on a ring

Abstract

In this paper, we prove a conjecture by Aas and Linusson on 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 conjectures in terms of placements of numbers in triangular arrays. Further, we use projections to calculate correlations in the continuous multispecies TASEP using a distribution on these placements.