A generalized Asymmetric Exclusion Process with U_q(\mathfraksl₂) stochastic duality

2014/07/12 by Gioia Carinci, Cristian Giardinà, Carinci, Gioia +5 · 1 citation
Mathematics · #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum Algebra (math.QA) #Random Matrices and Applications #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1407.3367

openalex publication_date 2014/07/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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∈ (0,1) and where at most 2j∈ℕ particles per site are allowed. The process is constructed from a (2j+1)-dimensional representation of a quantum Hamiltonian with U_q(\mathfraksl₂) invariance by applying a suitable ground-state transformation. After showing basic properties of the process ASEP(q,j), we prove self-duality with several self-duality functions constructed from the symmetries of the quantum Hamiltonian. By making use of the self-duality property we compute the first q-exponential moment of the current for step initial conditions (both a shock or a rarefaction fan) as well as when the process is started from an homogeneous product measure.

Cited by

• ASEP(q,j) converges to the KPZ equation

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