• Corpus ID: 214693265

Shock fluctuations in TASEP under a variety of time scalings

@article{Bufetov2020ShockFI,
  title={Shock fluctuations in TASEP under a variety of time scalings},
  author={Alexey Bufetov and Patrik L. Ferrari},
  journal={arXiv: Probability},
  year={2020}
}
We consider the totally asymmetric simple exclusion process (TASEP) with two different initial conditions with shock discontinuities, made by block of fully packed particles. Initially a second class particle is at the left of a shock discontinuity. Using multicolored TASEP we derive an exact formulas for the distribution of the second class particle and colored height functions. These are given in terms of the height function at different positions of a single TASEP configuration. We study the… 

Figures from this paper

Cutoff profile of ASEP on a segment
TLDR
This paper studies the mixing behavior of the Asymmetric Simple Exclusion Process (ASEP) on a segment of length N and finds that for particle densities in (0, 1), the total-variation cutoff window of ASEP is N 1 / 3 and the cutoff profile is 1-F GUE, where F GUE is the Tracy-Widom distribution function.
The half-space Airy stat process
Shift-Invariance of the Colored TASEP and Finishing Times of the Oriented Swap Process
We prove a new shift-invariance property of the colored TASEP. From the shift-invariance of the colored six-vertex model (proved in Borodin-Gorin-Wheeler or Galashin), one can get a shift-invariance

References

SHOWING 1-10 OF 39 REFERENCES
Anomalous shock fluctuations in TASEP and last passage percolation models
We consider the totally asymmetric simple exclusion process with initial conditions and/or jump rates such that shocks are generated. If the initial condition is deterministic, then the shock at time
Statistics of TASEP with Three Merging Characteristics
In this paper we consider the totally asymmetric simple exclusion process, with non-random initial condition having three regions of constant densities of particles. From left to right, the densities
Finite GUE Distribution with Cut-Off at a Shock
We consider the totally asymmetric simple exclusion process with initial conditions generating a shock. The fluctuations of particle positions are asymptotically governed by the randomness around the
Large time asymptotics of growth models on space-like paths I: PushASEP
We consider a new interacting particle system on the one-dimensional lattice that interpolates between TASEP and Toom's model: A particle cannot jump to the right if the neighboring site is occupied,
Current fluctuations for TASEP: A proof of the Pr\
We consider the family of two-sided Bernoulli initial conditions for TASEP which, as the left and right densities (p-, ρ+) are varied, give rise to shock waves and rarefaction fans—the two phenomena
Transition to Shocks in TASEP and Decoupling of Last Passage Times
We consider the totally asymmetric simple exclusion process in a critical scaling parametrized by $a\geq0$, which creates a shock in the particle density of order $aT^{-1/3},$ $T$ the observation
The TASEP speed process.
In the multi-type totally asymmetric simple exclusion process (TASEP), each site ofZ is occupied by a labeled particle, and two neighboring particles are int erchanged at rate one if their labels are
Limit law of a second class particle in TASEP with non-random initial condition
We consider the totally asymmetric simple exclusion process (TASEP) with non-random initial condition having density $\rho$ on $\mathbb{Z}_-$ and $\lambda$ on $\mathbb{Z}_+$, and a second class
Limit process of stationary TASEP near the characteristic line
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
Universality of the GOE Tracy-Widom distribution for TASEP with arbitrary particle density
TLDR
GOE Tracy-Widom universality of the one-point fluctuations of the associated height function is shown, phrased in last passage percolation language is the universality for the point-to-line problem where the line has an arbitrary slope.
...
...