Stochastic duality of ASEP with two particle types via symmetry of quantum groups of rank two

Abstract

We study two generalizations of the asymmetric simple exclusion process with two types of particles. Particles of type 1 can jump over particles of type 2, while particles of type 2 can only influence the jump rates of particles of type 1. We prove that the processes are self-dual and explicitly write the duality function. As an application, an expression for the r-th moment of the exponentiated current is written in terms of r-particle evolution. The construction and proofs of duality are accomplished using symmetry of the quantum groups $U_q({\mathfrak{gl}}_3)$ and $U_q({\mathfrak{sp}}_4)$, with each node in the Dynkin diagram corresponding to a particle type, and the number of edges corresponding to the jump rates.

References in corpus (6)

• Stochastic higher spin vertex models on the line
• Algebraic Bethe Ansatz for the two species ASEP with different hopping rates
• Self-Duality for the Two-Component Asymmetric Simple Exclusion Process
• Determinant representation for some transition probabilities in the TASEP with second class particles
• Quantum algebra symmetry of the ASEP with second-class particles
• On the Distribution of a Second Class Particle in the Asymmetric Simple Exclusion Process

Cited by in corpus (13)

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• A Multi-species ASEP(q,j) and q-TAZRP with Stochastic Duality
• Koornwinder polynomials and the stationary multi-species asymmetric exclusion process with open boundaries
• Self-duality of Markov processes and intertwining functions
• Integrable stochastic dualities and the deformed Knizhnik-Zamolodchikov equation
• Limiting current distribution for a two species asymmetric exclusion process
• Regularity comparison of symbolic powers, integral closure of powers and powers of edge ideals
• Duality relations for the ASEP conditioned on a low current
• Orthogonal polynomial duality of a two-species asymmetric exclusion process
• Intertwinings for Continuum Particle Systems: an Algebraic Approach
• Explicit Central Elements of $U_q(\mathfrak{gl}(N+1))$