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We prove duality relations for two interacting particle systems: the $q$-deformed totally asymmetric simple exclusion process ($q$-TASEP) and the asymmetric simple exclusion process (ASEP).
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Bangerezako, G.G. (2007). An introduction to q q -difference equations. Preprint. Available at http://perso.uclouvain.be/alphonse.magnus/gbang/qbook712.pdf
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Tracy, Craig A.C. A. andWidom, HaroldH. (2008). A Fredholm determinant representation in ASEP. J. Stat. Phys. 132 291–300
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Tracy, Craig A.C. A. andWidom, HaroldH. (2009). Asymptotics in ASEP with step initial condition. Comm. Math. Phys. 290 129–154
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