Riemann surface for TASEP with periodic boundaries

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.

arXiv comment31 pages, 5 figures, 3 tables

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Cited by in corpus (6)

• Dualities in quantum integrable many-body systems and integrable probabilities -- I
• KPZ fluctuations in finite volume
• Riemann surfaces for integer counting processes
• From the Riemann surface of TASEP to ASEP
• Approach to stationarity for the KPZ fixed point with boundaries
• Probability of a single current