# Self-Duality for the Two-Component Asymmetric Simple Exclusion Process

@article{Belitsky2015SelfDualityFT, title={Self-Duality for the Two-Component Asymmetric Simple Exclusion Process}, author={Vladimir Belitsky and G.M.Schutz}, journal={arXiv: Probability}, year={2015} }

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 measures of the process and the symmetry of the generator under the quantum algebra $U_q[\mathfrak{gl}_3]$. We construct all invariant measures in explicit form and discuss some of their properties. We also prove a sum rule for the duality functions.

## 30 Citations

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We consider a two-component asymmetric simple exclusion process (ASEP) on a finite lattice with reflecting boundary conditions. For this process, which is equivalent to the ASEP with second-class…

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We study two generalizations of the asymmetric simple exclusion process (ASEP) with two types of particles, which will be called type A2 ASEP and type C2 ASEP. Particles of type 1 force particles of…

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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…

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Duality relations for the ASEP conditioned on a low current

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We consider the asymmetric simple exclusion process (ASEP) on a finite lattice with periodic boundary conditions, conditioned to carry an atypically low current. For an infinite discrete set of…

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We show that quantum Schur-Weyl duality leads to Markov duality for a variety of asymmetric interacting particle systems. In particular, we consider three cases:
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We consider a two-component asymmetric simple exclusion process (ASEP) on a finite lattice with reflecting boundary conditions. For this process, which is equivalent to the ASEP with second-class…

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In previous work the authors, using the Bethe Ansatz, found for the N-particle asymmetric simple exclusion process on the integers a formula—a sum of multiple integrals—for the probability that a…

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We study a new process, which we call ASEP$(q,j)$, where particles move asymmetrically on a one-dimensional integer lattice with a bias determined by $q\in (0,1)$ and where at most $2j\in\mathbb{N}$…

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We study the transition probabilities for the totally asymmetric simple exclusion process (TASEP) on the infinite integer lattice with a finite, but arbitrary number of first and second class…

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We consider the exponential moments of integrated currents of 1D asymmetric simple exclusion process using the duality found by Schütz. For the ASEP on the infinite lattice we show that the nth…