Current Distribution and random matrix ensembles for an integrable asymmetric fragmentation process

Abstract

We calculate the time-evolution of a discrete-time fragmentation process in which clusters of particles break up and reassemble and move stochastically with size-dependent rates. In the continuous-time limit the process turns into the totally asymmetric simple exclusion process (only pieces of size 1 break off a given cluster). We express the exact solution of master equation for the process in terms of a determinant which can be derived using the Bethe ansatz. From this determinant we compute the distribution of the current across an arbitrary bond which after appropriate scaling is given by the distribution of the largest eigenvalue of the Gaussian unitary ensemble of random matrices. This result confirms universality of the scaling form of the current distribution in the KPZ universality class and suggests that there is a link between integrable particle systems and random matrix ensembles.

11 pages

References in corpus (12)

• Level-Spacing Distributions and the Airy Kernel
• Shape Fluctuations and Random Matrices
• Universal Distributions for Growth Processes in 1+1 Dimensions and Random Matrices
• Phase Transitions in one-dimensional nonequilibrium systems
• Exact Solution of the Master Equation for the Asymmetric Exclusion Process
• Critical phenomena and universal dynamics in one-dimensional driven diffusive systems with two species of particles
• Fluctuations of a one-dimensional polynuclear growth model in a half space
• Boundary-Induced Phase Transitions in Equilibrium and Non-Equilibrium Systems
• A two--parametric family of asymmetric exclusion processes and its exact solution
• Aggregate formation in a system of coagulating and fragmenting particles with mass-dependent diffusion rates
• The Kasteleyn model and a cellular automaton approach to traffic flow
• Broken Ergodicity in a Stochastic Model with Condensation

Cited by in corpus (55)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport
• Fluctuation properties of the TASEP with periodic initial configuration
• A pedestrian's view on interacting particle systems, KPZ universality, and random matrices
• Spatial correlations of the 1D KPZ surface on a flat substrate
• Universal cumulants of the current in diffusive systems on a ring
• Integral Formulas for the Asymmetric Simple Exclusion Process
• Exact Current Statistics of the ASEP with Open Boundaries
• Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition
• Current fluctuations in the zero-range process with open boundaries
• Fluctuations of the one-dimensional polynuclear growth model with external sources
• The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice Gases
• Fluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques
• On integrability of zero-range chipping models with factorized steady state
• Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition
• Some Exact Results for the Exclusion Process
• Determinant solution for the Totally Asymmetric Exclusion Process with parallel update
• Determinantal transition kernels for some interacting particles on the line
• Bethe ansatz and current distribution for the TASEP with particle-dependent hopping rates
• A multi-dimensional Markov chain and the Meixner ensemble
• Determinant solution for the Totally Asymmetric Exclusion Process with parallel update II. Ring geometry
• Kardar-Parisi-Zhang Universality of the Nagel-Schreckenberg Model
• Determinantal structures in the O'Connell-Yor directed random polymer model
• Random Matrices in 2D, Laplacian Growth and Operator Theory
• Exact Relaxation Dynamics in the Totally Asymmetric Simple Exclusion Process
• Determinant representation for some transition probabilities in the TASEP with second class particles
• The totally asymmetric exclusion process with generalized update
• TASEP and generalizations: Method for exact solution
• Multi-point distribution of periodic TASEP
• Long time asymptotics of the totally asymmetric simple exclusion process
• Bethe Ansatz in the Bernoulli Matching Model of Random Sequence Alignment
• Distribution of a particle's position in the ASEP with the {alternating} initial condition
• The transition probability and the probability for the left-most particle's position of the q-TAZRP
• The current distribution of the multiparticle hopping asymmetric diffusion model
• Exact solution of the Bernoulli matching model of sequence alignment
• Formulas and Asymptotics for the Asymmetric Simple Exclusion Process
• Family of Commuting Operators for the Totally Asymmetric Exclusion Process
• Universal exit probabilities in the TASEP
• Generalized Green Functions and current correlations in the TASEP
• Fluctuations in the discrete TASEP with periodic initial configurations and the Airy_1 process
• From Vicious Walkers to TASEP
• Airy process with wanderers, KPZ fluctuations, and a deformation of the Tracy--Widom GOE distribution
• Green functions for the TASEP with sublattice parallel update
• Phase separation transition of reconstituting k-mers in one dimension
• Transition Probabilities of the Bethe Ansatz Solvable Interacting Particle Systems
• The KPZ fixed point for discrete time TASEPs
• Periodic TASEP with general initial conditions
• Connected Operators for the Totally Asymmetric Exclusion Process
• Dimers and orthogonal polynomials: connections with random matrices
• Skew Howe duality and limit shapes of Young diagrams
• Nonstationary generalized TASEP in KPZ and jamming regimes
• Fluctuations of TASEP on a ring in relaxation time scale
• Soft edge results for longest increasing paths on the planar lattice
• Nonequilibrium phases and quantum correlations in synthetic transport models
• Two Speed TASEP with Step Initial Condition