Limiting current distribution for a two species asymmetric exclusion process
arXiv:2104.00026 · doi:10.1007/s00220-022-04408-8
Abstract
We study current fluctuations of a two-species asymmetric exclusion process, known as the Arndt-Heinzel-Rittenberg model. For a step-Bernoulli initial condition with finite number of particles, we provide an explicit multiple integral expression for a certain joint current probability distribution. By performing an asymptotic analysis we prove that the joint current distribution is given by a product of a Gaussian and a GUE Tracy-Widom distribution in the long time limit, as predicted by non-linear fluctuating hydrodynamics.
arXiv comment65 pages, 12 figures
References in corpus (54)
- Level-Spacing Distributions and the Airy Kernel
- Shape Fluctuations and Random Matrices
- Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
- The one-dimensional KPZ equation: an exact solution and its universality
- Nonlinear fluctuating hydrodynamics for anharmonic chains
- Asymptotics in ASEP with Step Initial Condition
- Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
- Fluctuation properties of the TASEP with periodic initial configuration
- Exact Solution of the Master Equation for the Asymmetric Exclusion Process
- An exact solution for the KPZ equation with flat initial conditions
- Exact results for anomalous transport in one dimensional Hamiltonian systems
- Exact height distributions for the KPZ equation with narrow wedge initial condition
- Spatial correlations of the 1D KPZ surface on a flat substrate
- The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics
- Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries
- Integral Formulas for the Asymmetric Simple Exclusion Process
- A Fredholm Determinant Representation in ASEP
- From duality to determinants for q-TASEP and ASEP
- Stationary distributions of multi-type totally asymmetric exclusion processes
- Transition between Airy_1 and Airy_2 processes and TASEP fluctuations
- The crossover regime for the weakly asymmetric simple exclusion process
- Spontaneous Breaking of Translational Invariance in One-Dimensional Stationary States on a Ring
- Stochastic higher spin vertex models on the line
- On integrability of zero-range chipping models with factorized steady state
- Spatial Particle Condensation for an Exclusion Process on a Ring
- Spontaneous Breaking of Translational Invariance and Spatial Condensation in Stationary States on a Ring: I. The Neutral System
- A multi-species asymmetric simple exclusion process and its relation to traffic flow
- On the Yang-Baxter equation for the six-vertex model
- Asymmetric Simple Exclusion Process and Modified Random Matrix Ensembles
- Exact solution of an exclusion process with three classes of particles and vacancies
- Matrix product solution of the multispecies partially asymmetric exclusion process
- Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries
- Coupled Kardar-Parisi-Zhang Equations in One Dimension
- On ASEP with Step Bernoulli Initial Condition
- Matrix product formula for Macdonald polynomials
- Spectrum in multi-species asymmetric simple exclusion process on a ring
- Shift-invariance for vertex models and polymers
- Algebraic Bethe Ansatz for the two species ASEP with different hopping rates
- Lectures on Integrable probability: Stochastic vertex models and symmetric functions
- Exact confirmation of 1D nonlinear fluctuating hydrodynamics for a two-species exclusion process
- Self-Duality for the Two-Component Asymmetric Simple Exclusion Process
- An algebraic construction of duality functions for the stochastic U_q(A_n^{(1)}) vertex model and its degenerations
- Searching for the Tracy-Widom distribution in nonequilibrium processes
- On the asymmetric simple exclusion process with multiple species
- Multispecies TASEP and the tetrahedron equation
- Stochastic duality of ASEP with two particle types via symmetry of quantum groups of rank two
- Quantum algebra symmetry of the ASEP with second-class particles
- KPZ statistics of second class particles in ASEP via mixing
- Integrable stochastic dualities and the deformed Knizhnik-Zamolodchikov equation
- Multispecies totally asymmetric zero range process: I. Multiline process and combinatorial
- Dynamic Screening in a Two-Species Asymmetric Exclusion Process
- Observables of stochastic colored vertex models and local relation
- - relations for the integrable two-species asymmetric simple exclusion process with open boundaries
- Probability distributions of multi-species q-TAZRP and ASEP as double cosets of parabolic subgroups