# Nonstationary Generalized TASEP in KPZ and Jamming Regimes

@article{Derbyshev2020NonstationaryGT, title={Nonstationary Generalized TASEP in KPZ and Jamming Regimes}, author={A. E. Derbyshev and A. M. Povolotsky}, journal={Journal of Statistical Physics}, year={2020}, volume={185} }

We study the model of the totally asymmetric exclusion process with generalized update, which compared to the usual totally asymmetric exclusion process, has an additional parameter enhancing clustering of particles. We derive the exact multiparticle distributions of distances travelled by particles on the infinite lattice for two types of initial conditions: step and alternating ones. Two different scaling limits of the exact formulas are studied. Under the first scaling associated to Kardar…

## References

SHOWING 1-10 OF 82 REFERENCES

### Generalizations of TASEP in Discrete and Continuous Inhomogeneous Space

- MathematicsCommunications in Mathematical Physics
- 2019

We investigate a rich new class of exactly solvable particle systems generalizing the Totally Asymmetric Simple Exclusion Process (TASEP). Our particle systems can be thought of as new exactly…

### Emergence of jams in the generalized totally asymmetric simple exclusion process.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2015

A crossover parameter is identified and the large deviation function for particle current is derived, which interpolates between the case considered by Derrida-Lebowitz and a single-particle diffusion.

### Tracy-Widom limit of $q$-Hahn TASEP

- Mathematics
- 2014

We consider the $q$-Hahn TASEP which is a three-parameter family of discrete time interacting particle systems. The particles jump to the right independently according to a certain $q$-Binomial…

### Integral Formulas for the Asymmetric Simple Exclusion Process

- Mathematics
- 2008

In this paper we obtain general integral formulas for probabilities in the asymmetric simple exclusion process (ASEP) on the integer lattice $${\mathbb{Z}}$$ with nearest neighbor hopping rates p to…

### Universal exit probabilities in the TASEP

- Mathematics
- 2012

We study the joint exit probabilities of particles in the totally asymmetric simple exclusion process (TASEP) from space–time sets of a given form. We extend previous results on the space–time…

### Limit process of stationary TASEP near the characteristic line

- Mathematics
- 2010

The totally asymmetric simple exclusion process (TASEP) on\input amssym ${\Bbb Z}$ with the Bernoulli‐ρ measure as an initial condition, 0 < ρ < 1, is stationary. It is known that along the…

### The Kardar-Parisi-Zhang equation and universality class

- Mathematics
- 2011

Brownian motion is a continuum scaling limit for a wide class of random processes, and there has been great success in developing a theory for its properties (such as distribution functions or…

### Fluctuations for stationary q-TASEP

- MathematicsProbability Theory and Related Fields
- 2018

We consider the q-totally asymmetric simple exclusion process (q-TASEP) in the stationary regime and study the fluctuation of the position of a particle. We first observe that the problem can be…

### Matrix-product ansatz for the totally asymmetric simple exclusion process with a generalized update on a ring.

- MathematicsPhysical review. E
- 2016

A quadratic algebra is constructed and an analytic expression for the finite-size pair correlation function is obtained in the limit of irreversible aggregation p[over ̃]→1, when the stationary configurations contain just one cluster.

### Transition between Airy1 and Airy2 processes and TASEP fluctuations

- Computer Science
- 2007

In this paper the totally asymmetric simple exclusion process is considered, a model in the KPZ universality class, and its one‐point distribution is a new interpolation between GOE and GUE edge distributions.