论文标题
弱噪声理论中的整合性
Integrability in the weak noise theory
论文作者
论文摘要
我们考虑了与弗里德林 - 温特兹尔大偏差原理（LDP）相关的变异问题（随机热方程（SHA）。对于一般的初始末端条件类别，我们表明存在这种变分问题的最小化器，任何最小化器都解决了虚构时间非线性schrödinger方程的系统。该系统是可集成的。利用可集成性，我们证明了物理学工作的公式Krajenbrink和le doussal（2021）（2021年）都为变异问题的每个最小化提供了。作为一个应用程序，我们考虑了Delta初始条件的SHE的Freidlin-Wentzell LDP。根据对反射系数的极点的技术假设，我们证明了物理学作品中预测的单点速率函数的明确表达，Majumdar，Majumdar，Rosso和Schehr（2016）以及Krajenbrink和Krajenbrink和Le Doussal（2021）。在相同的假设下，我们对上尾限制中最可能的形状进行了详细的详细估计。
We consider the variational problem associated with the Freidlin--Wentzell Large Deviation Principle (LDP) for the Stochastic Heat Equation (SHE). For a general class of initial-terminal conditions, we show that a minimizer of this variational problem exists, and any minimizer solves a system of imaginary-time Nonlinear Schrödinger equations. This system is integrable. Utilizing the integrability, we prove that the formulas from the physics work Krajenbrink and Le Doussal (2021) hold for every minimizer of the variational problem. As an application, we consider the Freidlin--Wentzell LDP for the SHE with the delta initial condition. Under a technical assumption on the poles of the reflection coefficients, we prove the explicit expression for the one-point rate function that was predicted in the physics works Le Doussal, Majumdar, Rosso, and Schehr (2016) and Krajenbrink and Le Doussal (2021). Under the same assumption, we give detailed pointwise estimates of the most probable shape in the upper-tail limit.
