A generalized Asymmetric Exclusion Process with $U_q(\mathfrak{sl}_2)$ stochastic duality

Gioia Carinci; Cristian Giardina'; Frank Redig; Tomohiro Sasamoto

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arXiv · 1407.3367

A generalized Asymmetric Exclusion Process with $U_q(\mathfrak{sl}_2)$ stochastic duality

Gioia Carinci·Cristian Giardina'·Frank Redig·Tomohiro Sasamoto

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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 $q\in (0,1)$ and where at most $2j\in\mathbb{N}$ particles per site are allowed. The process is constructed from a $(2j+1)$-dimensional representation of a quantum Hamiltonian with $U_q(\mathfrak{sl}_2)$ 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.

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BibTeX RIS

Gioia Carinci, Cristian Giardina', Frank Redig, Tomohiro Sasamoto. 2014-07-12. A generalized Asymmetric Exclusion Process with $U_q(\mathfrak{sl}_2)$ stochastic duality. https://arxiv.org/abs/1407.3367

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