Abstract
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.
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