Related papers: Painlev\'e Functions in Statistical Physics
The asymmetric simple exclusion process (ASEP) is a paradigmatic nonequilibrium many-body system that describes the asymmetric random walk of particles with exclusion interactions in a lattice. Although the ASEP is recognized as an exactly…
The totally asymmetric simple exclusion process (TASEP) is a stochastic model for the unidirectional dynamics of interacting particles on a $1$D-lattice that is much used in systems biology and statistical physics. Its master equation…
We study the asymmetric simple exclusion process (ASEP) on a segment $\{1,\ldots,b_N\}$ and are interested in its total variation distance to equilibrium when started from an initial configuration $\xi^{N}$. We provide a general result…
For the asymmetric simple exclusion process on the integer lattice with two-sided Bernoulli initial condition, we derive exact formulas for the following quantities: (1) the probability that site x is occupied at time t; (2) a correlation…
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 t will have a width of order t^{1/3}. We…
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…
The totally asymmetric simple exclusion process (TASEP) is a paradigmatic lattice model for one-dimensional particle transport subject to excluded-volume interactions. Solving the inhomogeneous TASEP in which particles' hopping rates vary…
We consider the asymmetric simple exclusion process (ASEP) on a semi-infinite chain which is coupled at the end to a reservoir with a particle density that changes periodically in time. It is shown that the density profile assumes a…
We study the fluctuation properties of the asymmetric simple exclusion process (ASEP) on an infinite one-dimensional lattice. When $N$ particles are initially situated in the negative region with a uniform density $\rho_-=1$, Johansson…
We study a two-component asymmetric simple exclusion process (ASEP) that is equivalent to the ASEP with second-class particles. We prove self-duality with respect to a family of duality functions which are shown to arise from the reversible…
Introduced in the late 1960's, the asymmetric exclusion process (ASEP) is an important model from statistical mechanics which describes a system of interacting particles hopping left and right on a one-dimensional lattice of n sites with…
We study the $n$-component priority asymmetric simple exclusion process ($n$-ASEP) with reflecting boundaries. We obtain all invariant measures in explicit form and prove reversibility. Using the symmetry of the generator of the process…
We obtain the large deviation functional of a density profile for the asymmetric exclusion process of L sites with open boundary conditions when the asymmetry scales like 1/L. We recover as limiting cases the expressions derived recently…
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 time. When starting from step initial data,…
In this paper we study the asymptotic behavior of the Asymmetric Simple Exclusion Process (=ASEP) with finitely many particles. It turns out that a certain randomized initial condition is the most amenable to such an analysis. Our main…
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 was shown that the probability distribution…
We consider the one-dimensional asymmetric simple exclusion process (ASEP) in which particles jump to the right at rate $p\in(1/2,1]$ and to the left at rate $1-p$, interacting by exclusion. In the initial state there is a finite region…
We investigate the dynamics of the asymmetric simple exclusion process (ASEP) on a ring. The ASEP is equivalent to the derivative nonlinear Schr\"{o}dinger equation (DNLS), which is integrable quantum field theory, in the continuous limit.…
In this paper, we study a well known asymptotic limit in which the second Painlev\'e equation (P_II) becomes the first Painlev\'e equation (P_I). The limit preserves the Painlev\'e property (i.e. that all movable singularities of all…
We study the speed of convergence to equilibrium for the asymmetric simple exclusion process (ASEP) on a finite interval with one open boundary. We provide sharp estimates on the total-variation distance from equilibrium and verify that the…