Exceedingly large deviations of the totally asymmetric exclusion process

  title={Exceedingly large deviations of the totally asymmetric exclusion process},
  author={Stefano Olla and Li-Cheng Tsai},
  journal={Electronic Journal of Probability},
Consider the Totally Asymmetric Simple Exclusion Process (TASEP) on the integer lattice $ \mathbb{Z} $. We study the functional Large Deviations of the integrated current $ \mathsf{h}(t,x) $ under the hyperbolic scaling of space and time by $ N $, i.e., $ \mathsf{h}_N(t,\xi) := \frac{1}{N}\mathsf{h}(Nt,N\xi) $. As hinted by the asymmetry in the upper- and lower-tail large deviations of the exponential Last Passage Percolation, the TASEP exhibits two types of deviations. One type of deviations… 
Upper Tail Large Deviations in First Passage Percolation
For first passage percolation on ℤ2 with i.i.d. bounded edge weights, we consider the upper tail large deviation event, i.e., the rare situation where the first passage time between two points at
Lower tail of the KPZ equation
We provide the first tight bounds on the lower tail probability of the one point distribution of the KPZ equation with narrow wedge initial data. Our bounds hold for all sufficiently large times $T$
Upper-tail large deviation principle for the ASEP
We consider the asymmetric simple exclusion process (ASEP) on Z started from step initial data and obtain the exact Lyapunov exponents for H0(t), the integrated current of ASEP. As a corollary, we
Time evolution of the Kardar-Parisi-Zhang equation
The use of the non-linear SPDEs are inevitable in both physics and applied mathematics since many of the physical phenomena in nature can be effectively modeled in random and non-linear way. The
A Large deviation principle for last passage times in an asymmetric Bernoulli potential
We prove a large deviation principle and give an expression for the rate function, for the last passage time in a Bernoulli environment. The model is exactly solvable and its invariant version


Exact Large Deviation Functional of a Stationary Open Driven Diffusive System: The Asymmetric Exclusion Process
AbstractWe consider the asymmetric exclusion process (ASEP) in one dimension on sites i=1,...,N, in contact at sites i=1 and i=N with infinite particle reservoirs at densities ρa and ρb. As ρa and ρb
Exact Large Deviation Function in the Asymmetric Exclusion Process
By an extension of the Bethe ansatz method used by Gwa and Spohn, we obtain an exact expression for the large deviation function of the time averaged current for the fully asymmetric exclusion
Non-equilibrium behaviour of a many particle process: Density profile and local equilibria
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
Exact Solution of the Master Equation for the Asymmetric Exclusion Process
Using the Bethe ansatz, we obtain the exact solution of the master equation for the totally asymmetric exclusion process on an infinite one-dimensional lattice. We derive explicit expressions for the
Current Large Deviations for Asymmetric Exclusion Processes with Open Boundaries
We study the large deviation functional of the current for the Weakly Asymmetric Simple Exclusion Process in contact with two reservoirs. We compare this functional in the large drift limit to the
Scaling Limits of Interacting Particle Systems
1. An Introductory Example: Independent Random Walks.- 2. Some Interacting Particle Systems.- 3. Weak Formulations of Local Equilibrium.- 4. Hydrodynamic Equation of Symmetric Simple Exclusion
Level-spacing distributions and the Airy kernel
Large deviations for increasing sequences on the plane
Abstract. We prove a large deviation principle with explicit rate functions for the length of the longest increasing sequence among Poisson points on the plane. The rate function for lower tail
A variational principle for domino tilings
1.1. Description of results. A domino is a 1 x 2 (or 2 x 1) rectangle, and a tiling of a region by dominos is a way of covering that region with dominos so that there are no gaps or overlaps. In
TASEP with discontinuous jump rates
We prove a hydrodynamic limit for the totally asymmetric simple exclusion process with spatially inhomogeneous jump rates given by a speed function that may admit discontinuities. The limiting