Fluctuation exponents of the KPZ equation on a large torus

Dunlap, Alexander; Gu, Yu; Komorowski, Tomasz

doi:10.1002/cpa.22110

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Stationary Large Deviations1

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2024

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“…then implies 〈e sh(x,t) 〉 ≍ e t F (s) with F (s) = lim λ→∞ λ −1 F λ (s) the generating function of the stationary cumulants c st k = F (k) (0). At the KPZ fixed point with periodic boundary condition, the variance c st 2 = π/2 was first obtained in [348] for TASEP, see also [349] for a rigorous approach from the stochastic heat equation ( 4). An explicit parametric expression was eventually obtained for F (s) [186,226,[350][351][352][353][354] from various exactly solvable microscopic models.…”

Section: Stationary Large Deviationsmentioning

confidence: 99%

KPZ fluctuations in finite volume

Prolhac

2024

SciPost Phys. Lect. Notes

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These lecture notes, adapted from the habilitation thesis of the author, survey in a first part various exact results obtained in the past few decades about KPZ fluctuations in one dimension, with a special focus on finite volume effects describing the relaxation to its stationary state of a finite system starting from a given initial condition. The second part is more specifically devoted to an approach allowing to express in a simple way the statistics of the current in the totally asymmetric simple exclusion process in terms of a contour integral on a compact Riemann surface, whose infinite genus limit leads to KPZ fluctuations in finite volume.

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