Riemann surfaces for KPZ with periodic boundaries

Abstract

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 KdV solitons are discussed.

81 pages, 23 figures

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Cited by in corpus (9)

• The inverse scattering of the Zakharov-Shabat system solves the weak noise theory of the Kardar-Parisi-Zhang equation
• Half-space stationary Kardar-Parisi-Zhang equation
• KP governs random growth off a one dimensional substrate
• Integral formulas of ASEP and $q$-TAZRP on a ring
• Riemann surface for TASEP with periodic boundaries
• KPZ fluctuations in finite volume
• From the Riemann surface of TASEP to ASEP
• Upper-tail large deviation principle for the ASEP
• Mapping current and activity fluctuations in exclusion processes: consequences and open questions