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arXiv · 2104.13864

From the Riemann surface of TASEP to ASEP

Sylvain Prolhac
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Abstract

We consider the asymmetric simple exclusion process (ASEP) with forward hopping rate 1, backward hopping rate q and periodic boundary conditions. We show that the Bethe equations of ASEP can be decoupled, at all order in perturbation in the variable q, by introducing a formal Laurent series mapping the Bethe roots of the totally asymmetric case q=0 (TASEP) to the Bethe roots of ASEP. The probability of the height for ASEP is then written as a single contour integral on the Riemann surface on which symmetric functions of TASEP Bethe roots live.

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Sylvain Prolhac. 2021-04-28. From the Riemann surface of TASEP to ASEP. https://doi.org/10.1088/1751-8121%2Fac1ee6

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