论文标题
SHE的Lyapunov指数用于一般初始数据
Lyapunov exponents of the SHE for general initial data
论文作者
论文摘要
我们考虑$（1+1）$ - 尺寸随机热方程（SHA），具有乘法白噪声和Kardar-Parisi-Zhang（KPZ）方程的Cole-Hopf溶液。我们展示了计算SHE的Lyapunov指数的确切方法，其中包括大量的初始数据，其中包括任何有限的确定性阳性初始数据和固定初始数据。结果，我们为一般初始数据提供了KPZ方程的上尾大偏差率函数的精确公式。
We consider the $(1+1)$-dimensional stochastic heat equation (SHE) with multiplicative white noise and the Cole-Hopf solution of the Kardar-Parisi-Zhang (KPZ) equation. We show an exact way of computing the Lyapunov exponents of the SHE for a large class of initial data which includes any bounded deterministic positive initial data and the stationary initial data. As a consequence, we derive exact formulas for the upper tail large deviation rate functions of the KPZ equation for general initial data.
