Riemann surface for TASEP with periodic boundaries

TL;DR

This paper formulates the Bethe ansatz solution of periodic TASEP using a Riemann surface framework, providing explicit expressions for height fluctuation distributions via complex integrals.

Contribution

It introduces a novel Riemann surface approach to analyze the Bethe ansatz solution of periodic TASEP, linking integrable systems with algebraic geometry.

Findings

Explicit expression for joint height fluctuation distribution

Representation of solutions via Abelian integrals on Riemann surfaces

Simplification of complex probability distributions in TASEP

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.