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• W2790482530 abstract "We establish a large deviation principle for the Kardar-Parisi-Zhang (KPZ) equation, providing precise control over the left tail of the height distribution for narrow wedge initial condition. Our analysis exploits an exact connection between the KPZ one-point distribution and the Airy point process -- an infinite particle Coulomb-gas which arises at the spectral edge in random matrix theory. We develop the large deviation principle for the Airy point process and use it to compute, in a straight-forward and assumption-free manner, the KPZ large deviation rate function in terms of an electrostatic problem (whose solution we evaluate). This method also applies to the half-space KPZ equation, showing that its rate function is half of the full-space rate function. In addition to these long-time estimates, we provide rigorous proof of finite-time tail bounds on the KPZ distribution which demonstrate a crossover between exponential decay with exponent $3$ (in the shallow left tail) to exponent $5/2$ (in the deep left tail). The full-space KPZ rate function agrees with the one computed in Sasorov et al. [J. Stat. Mech, 063203 (2017)] via a WKB approximation analysis of a non-local, non-linear integro-differential equation generalizing Painlev'e II which Amir et al. [Comm. Pure Appl. Math. 64, 466 (2011)] related to the KPZ one-point distribution." @default.
• W2790482530 created "2018-03-29" @default.
• W2790482530 creator A5029914913 @default.
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• W2790482530 date "2018-08-08" @default.
• W2790482530 modified "2023-10-14" @default.
• W2790482530 title "Coulomb-Gas Electrostatics Controls Large Fluctuations of the Kardar-Parisi-Zhang Equation" @default.
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• W2790482530 doi "https://doi.org/10.1103/physrevlett.121.060201" @default.
• W2790482530 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/30141677" @default.
• W2790482530 hasPublicationYear "2018" @default.
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