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Riemann surfaces for KPZ with periodic boundaries

by Sylvain Prolhac

Submission summary

As Contributors: Sylvain Prolhac
Preprint link: scipost_201909_00001v1
Date submitted: 2019-09-04
Submitted by: Prolhac, Sylvain
Submitted to: SciPost Physics
Domain(s): Theoretical
Subject area: Mathematical Physics

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.

Current status:
Editor-in-charge assigned

Submission & Refereeing History

Submission scipost_201909_00001v1 on 4 September 2019

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