An Inhomogeneous Multispecies TASEP on a Ring
arXiv:1206.0316 · doi:10.1016/j.aam.2014.02.001
Abstract
We reinterpret and generalize conjectures of Lam and Williams as statements about the stationary distribution of a multispecies exclusion process on the ring. The central objects in our study are the multiline queues of Ferrari and Martin. We make some progress on some of the conjectures in different directions. First, we prove their conjectures in two special cases by generalizing the rates of the Ferrari-Martin transitions. Secondly, we define a new process on multiline queues, which have a certain minimality property. This gives another proof for one of the special cases; namely arbitrary jump rates for three species.
21 pages, 1 figure. major changes in exposition; definitions clarified and terminology made more self-contained
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Cited by in corpus (18)
- Matrix product formula for Macdonald polynomials
- Koornwinder polynomials and the stationary multi-species asymmetric exclusion process with open boundaries
- The shape of a random affine Weyl group element and random core partitions
- Combinatorial mappings of exclusion processes
- Inhomogeneous generalization of multispecies totally asymmetric zero range process
- Multiline queues with spectral parameters
- Modified Macdonald polynomials and the multispecies zero range process: II
- KPZ fluctuations in finite volume
- Inhomogenous Multispecies TASEP on a ring with spectral parameters
- Schubert polynomials and the inhomogeneous TASEP on a ring
- Multi species asymmetric simple exclusion process with impurity activated flips
- Bumping sequences and multispecies juggling
- Schubert polynomials, the inhomogeneous TASEP, and evil-avoiding permutations
- A product formula for the TASEP on a ring
- TASEP in any Weyl Group
- Combinatorics of a disordered two-species ASEP on a torus
- A bijection between evil-avoiding and rectangular permutations
- Ribosome Flow Model on a Ring