Facilitated exclusion process
@article{Baik2016FacilitatedEP, title={Facilitated exclusion process}, author={Jinho Baik and Guillaume Barraquand and Ivan Corwin and Toufic M. Suidan}, journal={arXiv: Probability}, year={2016} }
We study the Facilitated TASEP, an interacting particle system on the one dimensional integer lattice. We prove that starting from step initial condition, the position of the rightmost particle has Tracy Widom GSE statistics on a cube root time scale, while the statistics in the bulk of the rarefaction fan are GUE. This uses a mapping with last-passage percolation in a half-quadrant which is exactly solvable through Pfaffian Schur processes.
Our results further probe the question of how first…
24 Citations
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References
SHOWING 1-10 OF 20 REFERENCES
Pfaffian Schur processes and last passage percolation in a half-quadrant
- MathematicsThe Annals of Probability
- 2018
We study last passage percolation in a half-quadrant, which we analyze within the framework of Pfaffian Schur processes. For the model with exponential weights, we prove that the fluctuations of the…
Non-equilibrium behaviour of a many particle process: Density profile and local equilibria
- Mathematics
- 1981
SummaryOne considers a simple exclusion particle jump process on ℤ, where the underlying one particle motion is a degenerate random walk that moves only to the right. One starts with the…
The $q$-Hahn asymmetric exclusion process
- Mathematics
- 2015
We introduce new integrable exclusion and zero-range processes on the one-dimensional lattice that generalize the $q$-Hahn TASEP and the $q$-Hahn Boson (zero-range) process introduced in [Pov13] and…
Amplitude universality for driven interfaces and directed polymers in random media.
- PhysicsPhysical review. A, Atomic, molecular, and optical physics
- 1992
We present accurate estimates for the prefactors of the second and third moments of the height and free-energy fluctuations, as well as the leading correction to the growth rate and free energy per…
Facilitated asymmetric exclusion.
- MathematicsPhysical review letters
- 2010
It is shown that an initial density downstep develops into a rarefaction wave that can have a jump discontinuity at the leading edge, while an upstep results in a shock wave.
Current fluctuations for TASEP: A proof of the Pr\
- Mathematics
- 2009
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…
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…
Distributions of a particle’s position and their asymptotics in theq-deformed totally asymmetric zero range process with site dependent jumping rates
- MathematicsStochastic Processes and their Applications
- 2019
Asymptotics in ASEP with Step Initial Condition
- Mathematics
- 2008
In previous work the authors considered the asymmetric simple exclusion process on the integer lattice in the case of step initial condition, particles beginning at the positive integers. There it…
Active-absorbing-state phase transition beyond directed percolation: a class of exactly solvable models.
- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2009
A model of hardcore particles on a one-dimensional periodic lattice which undergoes an active-absorbing-state phase transition at finite density is introduced and it is shown that both the density of active sites and the survival probability vanish as the particle density is decreased below half.