从TASEP的黎曼曲面到ASEP的黎曼曲面
From the Riemann surface of TASEP to ASEP
摘要：
考虑前向跳频率为1、后向跳频率为q且具有周期边界条件的非对称简单排斥过程。我们表明，Bethe方程的ASEP可以解耦，在所有的顺序在变量q的扰动，通过引入一个正式的Laurent系列映射的Bethe根的完全不对称的情况下，q=0（TASEP）的Bethe根的ASEP。概率的高度为ASEP然后被写为一个单一的轮廓积分的黎曼表面上的对称功能的TASEP贝特根生活。
英文摘要：
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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