The Bethe ansatz solution of periodic TASEP is formulated in terms of a ramified covering from a Riemann surface to the sphere. The joint probability distribution of height fluctuations at n distinct times has in particular a relatively simple expression as a function of n variables on the Riemann surface built from exponentials of Abelian integrals, traced over the ramified covering and integrated on n nested contours in the complex plane.

中文翻译：

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具有周期性边界的TASEP的黎曼曲面

周期性TASEP的Bethe ansatz解决方案是根据从Riemann曲面到球体的分叉覆盖范围制定的。高度波动在n个不同时间的联合概率分布尤其具有一个相对简单的表达式，该函数是Riemann曲面上n个变量的函数，该变量是根据阿贝尔积分的指数建立的，其遍历了分叉的覆盖层并集成在复杂平面中的n个嵌套轮廓上。