The asymmetric Exclusion Process and Brownian Excursions
arXiv:cond-mat/0306078 · doi:10.1023/B:JOSS.0000019833.35328.b4
Abstract
We consider the totally asymmetric exclusion process (TASEP) in one dimension in its maximal current phase. We show, by an exact calculation, that the non-Gaussian part of the fluctuations of density can be described in terms of the statistical properties of a Brownian excursion. Numerical simulations indicate that the description in terms of a Brownian excursion remains valid for more general one dimensional driven systems in their maximal current phase.
23 pages, 1 figure, in latex, e-mail addresses: [email protected], [email protected], [email protected]
References in corpus (13)
- Phase transitions in an exactly soluble one-dimensional exclusion process
- Macroscopic fluctuation theory for stationary non equilibrium states
- The totally asymmetric exclusion process with extended objects, a model for protein synthesis
- Fluctuations in Stationary non Equilibrium States
- Free Energy Functional for Nonequilibrium Systems: An Exactly Solvable Case
- Steady-state selection in driven diffusive systems with open boundaries
- Representations of the quadratic Algebra and Partially Asymmetric Diffusion with Open Boundaries
- Partially Asymmetric Exclusion Process with Open Boundaries
- Exact solution of a partially asymmetric exclusion model using a deformed oscillator algebra
- Exact Free Energy Functional for a Driven Diffusive Open Stationary Nonequilibrium System
- Large deviation functional of the weakly asymmetric exclusion process
- Finite Dimensional Representations of the Quadratic Algebra: Applications to the Exclusion Process
- Exact Large Deviation Functional of a Stationary Open Driven Diffusive System: The Asymmetric Exclusion Process
Cited by in corpus (36)
- Non equilibrium steady states: fluctuations and large deviations of the density and of the current
- Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
- The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice Gases
- Current large deviations for Asymmetric Exclusion Processes with open boundaries
- The KPZ Limit of ASEP with Boundary
- Entropy of Open Lattice Systems
- Nonequilibrium stationary states and equilibrium models with long range interactions
- Half-space stationary Kardar-Parisi-Zhang equation
- Fluctuations in the weakly asymmetric exclusion process with open boundary conditions
- Dyck Paths, Motzkin Paths and Traffic Jams
- Continued Fractions and the Partially Asymmetric Exclusion Process
- Limit fluctuations for density of asymmetric simple exclusion processes with open boundaries
- Stochastic Dynamics of Discrete Curves and Multi-type Exclusion Processes
- Open ASEP in the Weakly Asymmetric Regime
- The Grand-Canonical Asymmetric Exclusion Process and the One-Transit Walk
- Stationary measures of the KPZ equation on an interval from Enaud-Derrida's matrix product ansatz representation
- Dual representations of Laplace transforms of Brownian excursion and generalized meanders
- Brownian bridges for late time asymptotics of KPZ fluctuations in finite volume
- Exact Large Deviations of the Current in the Asymmetric Simple Exclusion Process with Open Boundaries
- Approximating the stationary distribution of the ASEP with open boundaries
- KPZ fluctuations in finite volume
- Steady state of the KPZ equation on an interval and Liouville quantum mechanics
- Fluctuations of random Motzkin paths II
- Fluctuations of random Motzkin paths
- A two-line representation of stationary measure for open TASEP
- The parallel TASEP, fixed particle number and weighted Motzkin paths
- Approach to stationarity for the KPZ fixed point with boundaries
- Numerical Method for Accessing the Universal Scaling Function for a Multi-Particle Discrete Time Asymmetric Exclusion Process
- Stationary measure for six-vertex model on a strip
- Stationary Distribution of open Asymmetric Simple Exclusion Processes on an Interval as a marginal of a two-layer ensemble
- Limit theorems for random Motzkin paths near boundary
- Entropy of non-equilibrium stationary measures of boundary driven TASEP
- A combinatorial approach to jumping particles
- Limits of open ASEP stationary measures near a boundary
- Limit fluctuations of stationary measure of totally asymmetric simple exclusion process with open boundaries on the coexistence line
- Current fluctuations for the second class particle : joint statistics