Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userLimiting one-point distribution of periodic TASEP
141
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The relaxation time limit of the one-point distribution of the spatially periodic totally asymmetric simple exclusion process is expected to be the universal one point distribution for the models in the KPZ universality class in a periodic domain. Unlike the infinite line case, the limiting one point distribution depends non-trivially on the scaled time parameter. We study several properties of this distribution for the case of the periodic step and flat initial conditions. We show that the distribution changes from a Tracy-Widom distribution in the small time limit to the Gaussian distribution in the large time limit, and also obtain right tail estimate for all time. Furthermore, we establish a connection to integrable differential equations such as the KP equation, coupled systems of mKdV and nonlinear heat equations, and the KdV equation.
rate research
Read More
Recently Johansson and Rahman obtained the limiting multi-time distribution for the discrete polynuclear growth model, which is equivalent to discrete TASEP model with step initial condition. In this paper, we obtain a finite time multi-point distribution formula of continuous TASEP with general initial conditions in the space-time plane. We evaluate the limit of this distribution function when the times go to infinity proportionally for both step and flat initial conditions. These limiting distributions are expected to be universal for all the models in the Kardar-Parisi-Zhang universality class.
We consider the one-dimensional totally asymmetric simple exclusion process with an arbitrary initial condition in a spatially periodic domain, and obtain explicit formulas for the multi-point distributions in the space-time plane. The formulas are given in terms of an integral involving a Fredholm determinant. We then evaluate the large-time, large-period limit in the relaxation time scale, which is the scale such that the system size starts to affect the height fluctuations. The limit is obtained assuming certain conditions on the initial condition, which we show that the step, flat, and step-flat initial conditions satisfy. Hence, we obtain the limit theorem for these three initial conditions in the periodic model, extending the previous work on the step initial condition. We also consider uniform random and uniform-step random initial conditions.
We consider the geodesic of the directed last passage percolation with iid exponential weights. We find the explicit one point distribution of the geodesic location joint with the last passage times, and its limit when the size goes to infinity.
We consider TASEP in continuous time with non-random initial conditions and arbitrary fixed density of particles rho. We show GOE Tracy-Widom universality of the one-point fluctuations of the associated height function. The result phrased in last passage percolation language is the universality for the point-to-line problem where the line has an arbitrary slope.
We study the facilitated totally asymmetric exclusion process on the one dimensional integer lattice. We investigate the invariant measures and the limiting behavior of the process. We mainly derive the limiting distribution of the process when the initial distribution is the Bernoulli product measure with density $1/2$. We also prove that in the low density regime, the system finally converges to an absorbing state.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
