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.

31 pages, 5 figures, 3 tables

References in corpus (7)

• The one-dimensional KPZ equation and its universality class
• The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics
• Memory and universality in interface growth
• The Asymmetric Avalanche Process
• Riemann surfaces for KPZ with periodic boundaries
• Determinantal Representation of the Time-Dependent Stationary Correlation Function for the Totally Asymmetric Simple Exclusion Model
• Long time asymptotics of the totally asymmetric simple exclusion process

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