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- W4288090667 abstract "Consider the solution $mathcal{Z}(t,x)$ of the one-dimensional stochastic heat equation, with a multiplicative spacetime white noise, and with the delta initial data $mathcal{Z}(0,x) = delta(x)$. For any real $p>0$, we obtained detailed estimates of the $p$-th moment of $e^{t/12}mathcal{Z}(2t,0)$, as $ttoinfty$, and from these estimates establish the one-point upper-tail large deviation principle of the Kardar-Parisi-Zhang equation. The deviations have speed $t$ and rate function $Phi_+(y)=frac{4}{3}y^{3/2}$. Our result confirms the existing physics predictions [Le Doussal, Majumdar, Schehr 16] and also [Kamenev, Meerson, Sasorov 16]." @default.
- W4288090667 created "2022-07-28" @default.
- W4288090667 creator A5019309744 @default.
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- W4288090667 date "2019-10-21" @default.
- W4288090667 modified "2023-09-25" @default.
- W4288090667 title "Fractional moments of the Stochastic Heat Equation" @default.
- W4288090667 doi "https://doi.org/10.48550/arxiv.1910.09271" @default.
- W4288090667 hasPublicationYear "2019" @default.
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