Fractional moments of the stochastic heat equation
Fractional moments of the stochastic heat equation
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DOI：
10.1214/20-aihp1095
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发表时间：
2019-10
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影响因子：
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通讯作者：
Sayan Das;Li-Cheng Tsai
中科院分区：
文献类型：
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作者：
Sayan Das;Li-Cheng Tsai
考虑一维随机热方程的解$\mathcal{Z}（t，x）$，带有乘性时空白色噪声，δ初始数据$\mathcal{Z}（0，x）= \delta（x）$。对任意真实的p>0，我们得到了e^{t/12}\mathcal{Z}（2 t，0）$p阶矩的详细估计，并由此建立了Kardar-Parisi-Zhang方程的一点上尾大偏差原理.偏差具有速度$t$和速率函数$\Phi_+（y）=\frac{4}{3}y^{3/2}$。我们的结果证实了现有的物理预测[Le Doussal，Majumdar，Schehr 16]和[Kamenev，Meerson，Sasorov 16]。
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 $t\to\infty$, 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].