Riemann surfaces for KPZ with periodic boundaries

Riemann surfaces for KPZ with periodic boundaries

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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 longboard dancer deck 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 ic berlin eyewear st. louis stationary large deviations, particle-hole excitations and KdV solitons are discussed.