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Item Open Access Exact Formulas of the Transition Probabilities of the Multi-Species Asymmetric Simple Exclusion Process(arxiv, 2020) LEE, EunghyunWe find the formulas of the transition probabilities of the N-particle multi species asymmetric simple exclusion processes (ASEP), and show that the transition prob abilities are written as a determinant when the order of particles in the final state is the same as the order of particles in the initial state.Item Open Access INTEGRABILITY OF THE MULTI-SPECIES TASEP WITH SPECIES-DEPENDENT RATES(MDPI, 2021-08-27) Lee, EunghyunAssume that each species l has its own jump rate bl in the multi-species totally asymmetric simple exclusion process. We show that this model is integrable in the sense that the Bethe ansatz method is applicable to obtain the transition probabilities for all possible N-particle systems with up to N different species.