An inhomogeneous multispecies TASEP on a ring

@article{Ayyer2012AnIM,
  title={An inhomogeneous multispecies TASEP on a ring},
  author={Arvind Ayyer and Svante Linusson},
  journal={Adv. Appl. Math.},
  year={2012},
  volume={57},
  pages={21-43}
}
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References

SHOWING 1-10 OF 45 REFERENCES

Matrix Representation of the Stationary Measure for the Multispecies TASEP

In this work we construct the stationary measure of the N species totally asymmetric simple exclusion process in a matrix product formulation. We make the connection between the matrix product…

Tableaux combinatorics for the asymmetric exclusion process and Askey-Wilson polynomials

Introduced in the late 1960's, the asymmetric exclusion process (ASEP) is an important model from statistical mechanics which describes a system of interacting particles hopping left and right on a…

Stationary distributions of multi-type totally asymmetric exclusion processes

We consider totally asymmetric simple exclusion processes with n types of particle and holes (n-TASEPs) on Z and on the cycle Z N . Angel recently gave an elegant construction of the stationary…

Matrix product solution of an inhomogeneous multi-species TASEP

We study a multi-species exclusion process with inhomogeneous hopping rates and find a matrix product representation for the stationary state of this model. The matrices belong to the tensor algebra…

The matrix product solution of the multispecies partially asymmetric exclusion process

We find the exact solution for the stationary state measure of the partially asymmetric exclusion process on a ring with multiple species of particles. The solution is in the form of a matrix product…

Tableaux combinatorics for the asymmetric exclusion process

The stationary measure of a 2-type totally asymmetric exclusion process

Invariant measures for a two-species asymmetric process

We consider a process of two classes of particles jumping on a one-dimensional lattice. The marginal system of the first class of particles is the one-dimensional totally asymmetric simple exclusion…

A Markov chain on the symmetric group which is Schubert positive

We study a multivariate Markov chain on the symmetric group with remarkable enumerative properties. We conjecture that the stationary distribution of this Markov chain can be expressed in terms of…

Multiclass processes, dual points and M/M/1 queues

We consider the discrete Hammersley-Aldous-Diaconis process (HAD) and the totally asymmetric simple exclusion process (TASEP) in Z. The basic coupling induces a multiclass process which is useful in…