## 37 Citations

### Correlations in the continuous multispecies TASEP on a ring

- Mathematics
- 2022

. 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. We use the theory of multiline queues as…

### Correlations in the multispecies TASEP and a conjecture by Lam

- Mathematics
- 2016

We study correlations in the multispecies TASEP on a ring. Results on the correlation of two adjacent points prove two conjectures by Thomas Lam on (a) the limiting direction of a reduced random walk…

### Toric tableaux and the inhomogeneous two-species TASEP on a ring

- MathematicsAdv. Appl. Math.
- 2020

### Modified Macdonald polynomials and the multispecies zero range process: I

- Mathematics
- 2020

. In a previous part of this work, we gave a new tableau formula for the modiﬁed Macdonald polynomials r H λ p X ; q, t q , using a weight on tableaux involving the queue inversion (quinv) statistic.…

### Inhomogenous Multispecies TASEP on a ring with spectral parameters

- Mathematics
- 2016

We study an inhomogenous multispecies version of the Totally Asymmetric Simple Exclusion Process (TASEP) on a periodic oriented one dimensional lattice, which depends on two sets of parameters $({\bf…

### Some generalized juggling processes (extended abstract)

- Mathematics
- 2015

We consider generalizations of juggling Markov chains introduced by Ayyer, Bouttier, Corteel and Nunzi. We first study multispecies generalizations of all the finite models therein, namely the MJMC,…

### Some generalized juggling processes

- Mathematics
- 2015

We consider generalizations of juggling Markov chains introduced by Ayyer, Bouttier, Corteel and Nunzi. We first study multispecies generalizations of all the finite models therein, namely the MJMC,…

### Inhomogeneous Generalization of a Multispecies Totally Asymmetric Zero Range Process

- Mathematics
- 2016

The n-species totally asymmetric zero range process (n-TAZRP) on a one-dimensional periodic chain studied recently by the authors is a continuous time Markov process where arbitrary number of…

### Koornwinder polynomials and the stationary multi-species asymmetric exclusion process with open boundaries

- Mathematics
- 2016

We prove that the normalisation of the stationary state of the multi-species asymmetric simple exclusion process (mASEP) is a specialisation of a Koornwinder polynomial. As a corollary we obtain that…

### Schubert polynomials and the inhomogeneous TASEP on a ring

- Mathematics
- 2020

Consider a lattice of n sites arranged around a ring, with the n sites occupied by particles of weights {1, 2, . . . , n}; the possible arrangements of particles in sites thus corresponds to the n!…

## References

SHOWING 1-10 OF 45 REFERENCES

### Matrix Representation of the Stationary Measure for the Multispecies TASEP

- Mathematics
- 2008

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

- Mathematics
- 2009

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

- Mathematics
- 2007

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

- Mathematics
- 2013

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

- Mathematics
- 2008

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…

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

- MathematicsJ. Comb. Theory, Ser. A
- 2006

### Invariant measures for a two-species asymmetric process

- Mathematics
- 1994

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

- Mathematics
- 2011

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

- Mathematics
- 2005

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…