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}
}
  • S. Prolhac
  • Published 23 August 2019
  • Mathematics
  • SciPost Physics
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… 
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14 Citations
Background Citations
8
Methods Citations
3
Results Citations
1

14 Citations

Riemann surface for TASEP with periodic boundaries

  • S. Prolhac
  • Mathematics
    Journal 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…

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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

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

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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