论文标题
弱噪声理论的较低尾巴极限
A lower-tail limit in the weak noise theory
论文作者
论文摘要
我们考虑与弗里德林（Freidlin）相关的变异问题 - 温特（Wentzell）随机热方程（SHA）的大偏差原理。变分问题的最小化器的对数给出了kardar-parisi-zhang方程解决方案的最可能形状，其条件是达到某些不太可能的值。在适当的缩放下，将其带有Delta初始条件的SHE并在原点上调节其解决方案的值，我们证明，最小化器的对数会收敛到显式函数，因为我们将条件的值调整为$ 0 $。我们的结果证实了物理预测Kolokolov和Korshunov（2009），Meerson，Katzav和Vilenkin（2016），Kamenev，Meerson和Sasorov（2016）。
We consider the variational problem associated with the Freidlin--Wentzell Large Deviation Principle of the Stochastic Heat Equation (SHE). The logarithm of the minimizer of the variational problem gives the most probable shape of the solution of the Kardar--Parisi--Zhang equation conditioned on achieving certain unlikely values. Taking the SHE with the delta initial condition and conditioning the value of its solution at the origin at a later time, under suitable scaling, we prove that the logarithm of the minimizer converges to an explicit function as we tune the value of the conditioning to $ 0 $. Our result confirms the physics prediction Kolokolov and Korshunov (2009), Meerson, Katzav, and Vilenkin (2016), Kamenev, Meerson, and Sasorov (2016).
