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• W3105329413 abstract "We consider the weakly asymmetric limit of simple exclusion process with drift to the left, starting from step Bernoulli initial data with $rho_-<rho_+$ so that macroscopically one has a rarefaction fan. We study the fluctuations of the process observed along slopes in the fan, which are given by the Hopf--Cole solution of the Kardar-Parisi-Zhang (KPZ) equation, with appropriate initial data. For slopes strictly inside the fan, the initial data is a Dirac delta function and the one point distribution functions have been computed in [Comm. Pure Appl. Math. 64 (2011) 466-537] and [Nuclear Phys. B 834 (2010) 523-542]. At the edge of the rarefaction fan, the initial data is one-sided Brownian. We obtain a new family of crossover distributions giving the exact one-point distributions of this process, which converge, as $Tnearrowinfty$ to those of the Airy $mathcal{A}_{2to mathrm{BM}}$ process. As an application, we prove moment and large deviation estimates for the equilibrium Hopf-Cole solution of KPZ. These bounds rely on the apparently new observation that the FKG inequality holds for the stochastic heat equation. Finally, via a Feynman-Kac path integral, the KPZ equation also governs the free energy of the continuum directed polymer, and thus our formula may also be interpreted in those terms." @default.
• W3105329413 created "2020-11-23" @default.
• W3105329413 creator A5004274893 @default.
• W3105329413 creator A5068442476 @default.
• W3105329413 date "2013-05-01" @default.
• W3105329413 modified "2023-10-16" @default.
• W3105329413 title "Crossover distributions at the edge of the rarefaction fan" @default.
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• W3105329413 doi "https://doi.org/10.1214/11-aop725" @default.
• W3105329413 hasPublicationYear "2013" @default.
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