# Riemann surfaces for KPZ with periodic boundaries

@article{Prolhac2019RiemannSF, title={Riemann surfaces for KPZ with periodic boundaries}, author={Sylvain Prolhac}, journal={SciPost Physics}, year={2019} }

The Riemann surface for polylogarithms of half-integer index, which has the topology of an infinite dimensional hypercube, is studied in relation to one-dimensional KPZ universality in finite volume. Known exact results for fluctuations of the KPZ height with periodic boundaries are expressed in terms of meromorphic functions on this Riemann surface, summed over all the sheets of a covering map to an infinite cylinder. Connections to stationary large deviations, particle-hole excitations and…

## 14 Citations

### Riemann surface for TASEP with periodic boundaries

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2020

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…

### Integrable fluctuations in the KPZ universality class

- Mathematics
- 2022

A BSTRACT . The KPZ ﬁxed point is a scaling invariant Markov process which arises as the universal scaling limit of a broad class of models of random interface growth in one dimension, the…

### Riemann surface crossover for the spectral gaps of open TASEP

- Mathematics
- 2021

We consider the totally asymmetric simple exclusion process (TASEP) with open boundaries, at the edge of the maximal current (MC) phase. Using analytic continuations from the known stationary…

### KP governs random growth off a 1-dimensional substrate

- Mathematics, PhysicsForum of Mathematics, Pi
- 2022

Abstract The logarithmic derivative of the marginal distributions of randomly fluctuating interfaces in one dimension on a large scale evolve according to the Kadomtsev–Petviashvili (KP) equation.…

### Spectral gaps of open TASEP in the maximal current phase

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2020

We study spectral gaps of the one-dimensional totally asymmetric simple exclusion process (TASEP) with open boundaries in the maximal current phase. Earlier results for the model with periodic…

### Limiting one-point distribution of periodic TASEP

- MathematicsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques
- 2022

The relaxation time limit of the one-point distribution of the spatially periodic totally asymmetric simple exclusion process is expected to be the universal one point distribution for the models in…

### From the Riemann surface of TASEP to ASEP

- Mathematics
- 2021

We consider the asymmetric simple exclusion process (ASEP) with forward hopping rate 1, backward hopping rate q and periodic boundary conditions. We show that the Bethe equations of ASEP can be…

### Inverse Scattering of the Zakharov-Shabat System Solves the Weak Noise Theory of the Kardar-Parisi-Zhang Equation.

- MathematicsPhysical review letters
- 2021

The program of the weak noise theory is expanded, which maps the large deviations onto a nonlinear hydrodynamic problem, and its complete solvability is unveiled through a connection to the integrability of the Zakharov-Shabat system.

### Large deviations for the Kardar– Parisi–Zhang equation from the Kadomtsev–Petviashvili equation

- Mathematics
- 2020

Recently, Quastel and Remenik (2019 (arXiv:1908.10353)) found a remarkable relation between some solutions of the finite time Kardar–Parisi–Zhang (KPZ) equation and the Kadomtsev–Petviashvili (KP)…

### Integral Formulas of ASEP and q-TAZRP on a Ring

- MathematicsCommunications in Mathematical Physics
- 2020

In this paper, we obtain the transition probability formulas for the asymmetric simple exclusion process and the q-deformed totally asymmetric zero range process on the ring by applying the…

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