Asymmetric Simple Exclusion Process with Open Boundaries and Askey-Wilson Polynomials

Abstract

We study the one-dimensional asymmetric simple exclusion process (ASEP) with open boundary conditions. Particles are injected and ejected at both boundaries. It is clarified that the steady state of the model is intimately related to the Askey-Wilson polynomials. The partition function and the $n$-point functions are obtained in the integral form with four boundary parameters. The thermodynamic current is evaluated to confirm the conjectured phase diagram.

21 pages, 2 figures

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Cited by in corpus (72)

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• Stochastic six-vertex model in a half-quadrant and half-line open ASEP
• Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition
• Two-Species Asymmetric Simple Exclusion Process with Open Boundaries
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• Tableaux combinatorics for the asymmetric exclusion process and Askey-Wilson polynomials
• Matrix product formula for Macdonald polynomials
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• An algebraic construction of duality functions for the stochastic U_q(A_n^{(1)}) vertex model and its degenerations
• Open two-species exclusion processes with integrable boundaries
• Combinatorics of the two-species ASEP and Koornwinder moments
• Koornwinder polynomials and the stationary multi-species asymmetric exclusion process with open boundaries
• The Askey-Wilson algebra and its avatars
• Asymmetric Simple Exclusion Process with open boundaries and Quadratic Harnesses
• Integrable boundary conditions for multi-species ASEP
• Continued Fractions and the Partially Asymmetric Exclusion Process
• Limit fluctuations for density of asymmetric simple exclusion processes with open boundaries
• Combinatorial mappings of exclusion processes
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• The effect of detachment and attachment to a kink motion in the asymmetric simple exclusion process
• Open ASEP in the Weakly Asymmetric Regime
• Eigenstates of triangularisable open XXX spin chains and closed-form solutions for the steady state of the open SSEP
• Construction of a matrix product stationary state from solutions of finite size system
• Long time asymptotics of the totally asymmetric simple exclusion process
• Quasi-static limit for the asymmetric simple exclusion
• Matrix product solution to multi-species ASEP with open boundaries
• Stationary measures of the KPZ equation on an interval from Enaud-Derrida's matrix product ansatz representation
• Matrix product solution of a left-permeable two-species asymmetric exclusion process
• Tridiagonal representations of the q-oscillator algebra and Askey-Wilson polynomials
• Modified Macdonald polynomials and the multispecies zero range process: I
• Approximating the stationary distribution of the ASEP with open boundaries
• Multiline queues with spectral parameters
• On matrix product ansatz for Asymmetric Simple Exclusion Process with open boundary in the singular case
• KPZ fluctuations in finite volume
• Combinatorics of the asymmetric exclusion process on a semi-infinite lattice
• Tridiagonal Symmetries of Models of Nonequilibrium Physics
• From Quantum Affine Symmetry to Boundary Askey-Wilson Algebra and Reflection Equation
• Askey-Wilson signed measures and open ASEP in the shock region
• Active gating: rocking diffusion channels
• A Markov chain on permutations which projects to the PASEP
• Inhomogenous Multispecies TASEP on a ring with spectral parameters
• Hydrodynamic limit for asymmetric simple exclusion with accelerated boundaries
• Multi species asymmetric simple exclusion process with impurity activated flips
• Mixing times and cutoff for the TASEP in the high and low density phase
• The phase diagram for a multispecies left-permeable asymmetric exclusion process
• Higher Rank Askey-Wilson Algebras as Skein Algebras
• Numerical Estimation of the Current Large Deviation Function in the Asymmetric Simple Exclusion Process with Open Boundary Conditions
• A Generalized Dynamic Asymmetric Exclusion Process: Orthogonal Dualities and Degenerations
• New formulas for Macdonald polynomials via the multispecies exclusion and zero range processes
• The phase diagram for a class of multispecies permissive asymmetric exclusion processes
• Combinatorics of the three-parameter PASEP partition function
• Schubert polynomials, the inhomogeneous TASEP, and evil-avoiding permutations
• On perturbation around closed exclusion processes
• Stationary Distribution of open Asymmetric Simple Exclusion Processes on an Interval as a marginal of a two-layer ensemble
• Integrability in out-of-equilibrium systems
• Stationary measure for six-vertex model on a strip
• Steady state representations for the harmonic process
• Combinatorial formulas for the coefficients of the Al-Salam-Chihara polynomials
• Bi-orthogonal Polynomials and the Five parameter Asymmetric Simple Exclusion Process
• Bi-orthogonal Polynomial Sequences and the Asymmetric Simple Exclusion Process
• An insertion algorithm over staircase tableaux compatible with the ASEP's matrix ansatz
• Limit fluctuations of stationary measure of totally asymmetric simple exclusion process with open boundaries on the coexistence line
• Limits of open ASEP stationary measures near a boundary
• Mapping current and activity fluctuations in exclusion processes: consequences and open questions
• Orthogonal polynomials and the deformed Jordan plane
• Hidden Symmetries of Stochastic Models
• Matrix Ansatz, lattice paths and rook placements
• Ion transport through confined ion channels in the presence of immobile charges
• Quasi-static limit for a hyperbolic conservation law
• Boundary lines and Askey-Wilson type moments