2017/07/10 by Mandelshtam, Olya · 2 citations
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1707.02663
The inhomogeneous two-species TASEP on a ring is an exclusion process that describes particles of different species hopping clockwise on a ring with parameters giving the hopping rates for different species. We introduce a combinatorial object that we call toric rhombic alternative tableaux, which are certain fillings of tableaux on a triangular lattice tiled with rhombi, and are in bijection with the well-studied multiline queues of Ferrari and Martin. Using the tableaux, we obtain a formula for the stationary probabilities of this TASEP, which specializes to results of Ayyer and Linusson. We obtain, in addition, an explicit determinantal formula for these probabilities, and define a Markov chain on the tableaux that projects to the two-species TASEP on a ring.