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 roland blues cube amp 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 2006 scion xa catalytic converter to an infinite cylinder.Connections to stationary large deviations, particle-hole excitations and KdV solitons are discussed.