Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 139, 9 pages      arXiv:1809.07362      https://doi.org/10.3842/SIGMA.2020.139

Exact Formulas of the Transition Probabilities of the Multi-Species Asymmetric Simple Exclusion Process

Eunghyun Lee
Nazarbayev University, Nur-sultan, Kazakhstan

Received September 17, 2020, in final form December 15, 2020; Published online December 20, 2020

Abstract
We find the formulas of the transition probabilities of the $N$-particle multi-species asymmetric simple exclusion processes (ASEP), and show that the transition probabilities 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.

Key words: ASEP; multi-species ASEP; integrable probability.

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